{"id":12494,"date":"2024-02-29T18:15:50","date_gmt":"2024-02-29T10:15:50","guid":{"rendered":"http:\/\/www.aiersheng.cc\/?p=12494"},"modified":"2024-12-29T18:41:19","modified_gmt":"2024-12-29T10:41:19","slug":"%e5%b8%b8%e8%a7%81%e7%9a%84%e6%95%b0%e5%ad%a6%e5%85%ac%e5%bc%8f%e5%92%8c%e5%b7%a7%e8%ae%b0%e7%9a%84%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.aiersheng.cc\/?p=12494","title":{"rendered":"\u5e38\u89c1\u7684\u6570\u5b66\u516c\u5f0f\u548c\u5de7\u8bb0\u7684\u65b9\u6cd5"},"content":{"rendered":"

1. \u52a0\u6cd5\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $a+b=ca + b = c<\/span>a<\/span>+<\/span><\/span>b<\/span>=<\/span><\/span>c<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u52a0\u6cd5\u662f\u6700\u57fa\u7840\u7684\u8fd0\u7b97\uff0c\u7528\u6765\u6c42\u4e24\u4e2a\u6570\u7684\u548c\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\uff1a$23 + 45$
\n\u7b54\u6848\uff1a<\/strong>
\n$23 + 45 = 68$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u628a\u52a0\u6570\u62c6\u5206\u6210\u65b9\u4fbf\u7684\u6570\u6765\u52a0\u3002\u4f8b\u5982\uff1a$23 + 45$ \u53ef\u4ee5\u62c6\u6210 $20 + 40 = 60$ \u548c $3 + 5 = 8$\uff0c\u6700\u540e\u518d\u52a0 $60 + 8 = 68$\u3002<\/p>\n
\n
2. \u51cf\u6cd5\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $a\u2212b=c\u00a0 \u00a0 \u00a0a – b = c\u00a0 \u00a0 \u00a0 \u00a0<\/span>a<\/span>\u2212<\/span><\/span>b<\/span>=<\/span><\/span>c<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u51cf\u6cd5\u662f\u4ece\u4e00\u4e2a\u6570\u4e2d\u51cf\u53bb\u53e6\u4e00\u4e2a\u6570\uff0c\u7528\u6765\u6c42\u5dee\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\uff1a$75 – 28$
\n\u7b54\u6848\uff1a<\/strong>
\n$75 – 28 = 47$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u5c06\u51cf\u6570\u5206\u89e3\u6210\u6613\u8ba1\u7b97\u7684\u90e8\u5206\uff0c\u4f8b\u5982\uff1a$75 – 28$ \u53ef\u4ee5\u5206\u89e3\u4e3a $75 – 20 = 55$ \u548c $55 – 8 = 47$\u3002<\/p>\n
\n
3. \u4e58\u6cd5\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $a\u00d7b=ca \\times b = c<\/span>a<\/span>\u00d7<\/span><\/span>b<\/span>=<\/span><\/span>c<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u4e58\u6cd5\u662f\u5c06\u4e00\u4e2a\u6570\u4e0e\u53e6\u4e00\u4e2a\u6570\u76f8\u52a0\u82e5\u5e72\u6b21\u7684\u8fd0\u7b97\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\uff1a$6 \\times 8$
\n\u7b54\u6848\uff1a<\/strong>
\n$6 \\times 8 = 48$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u5229\u7528\u4e58\u6cd5\u5206\u914d\u5f8b\uff0c$6 \\times 8$ \u53ef\u4ee5\u5199\u6210 $6 \\times (5 + 3)$\uff0c\u7136\u540e\u5206\u522b\u8ba1\u7b97 $6 \\times 5 = 30$ \u548c $6 \\times 3 = 18$\uff0c\u6700\u540e\u52a0\u8d77\u6765\u5f97\u5230 $30 + 18 = 48$\u3002<\/p>\n
\n
4. \u9664\u6cd5\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $ab=c\\frac{a}{b} = c<\/span>b<\/span><\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>c<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u9664\u6cd5\u662f\u5c06\u4e00\u4e2a\u6570\u5e73\u5747\u5206\u6210\u82e5\u5e72\u4efd\uff0c\u6c42\u6bcf\u4efd\u7684\u5927\u5c0f\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\uff1a$48 \\div 6$
\n\u7b54\u6848\uff1a<\/strong>
\n$48 \\div 6 = 8$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u5c06\u88ab\u9664\u6570\u5206\u89e3\u3002\u4f8b\u5982\uff1a$48 \\div 6$ \u53ef\u4ee5\u5199\u6210 $(30 + 18) \\div 6$\uff0c\u7136\u540e\u5206\u522b\u8ba1\u7b97 $30 \\div 6 = 5$ \u548c $18 \\div 6 = 3$\uff0c\u6700\u540e\u5f97\u5230 $5 + 3 = 8$\u3002<\/p>\n
\n
5. \u5e73\u65b9\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $$(a+b)^2=$a^2+2ab+$b^2(a + b)^2 = a^2 + 2ab + b^2<\/span>(<\/span>a<\/span>+<\/span><\/span>b<\/span>)2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>2<\/span>ab<\/span>+<\/span><\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u5e73\u65b9\u516c\u5f0f\u7528\u4e8e\u5c55\u5f00\u4e8c\u9879\u5f0f\u7684\u5e73\u65b9\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u5c55\u5f00 $(3 + 5)^2$
\n\u7b54\u6848\uff1a<\/strong>
\n$3^2 + 2(3)(5) + 5^2 = 9 + 30 + 25 = 64$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u8bb0\u4f4f\u201c\u5e73\u65b9\u52a0\u4e24\u500d\u4e58\u79ef\u52a0\u5e73\u65b9\u201d\uff0c\u4f8b\u5982 $(a + b)^2$ \u5c31\u662f $a^2 + 2ab + b^2$\u3002<\/p>\n
\n
6. \u7acb\u65b9\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $(a+b)^3=a^3+3a2b+3ab2+b3(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3<\/span>(<\/span>a<\/span>+<\/span><\/span>b<\/span>)3<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>a<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>3<\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>b<\/span>+<\/span><\/span>3<\/span>a<\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>$
\u4f8b\u9898\uff1a<\/strong>
\n\u5c55\u5f00 $(2 + 3)^3$
\n\u7b54\u6848\uff1a<\/strong>
\n$2^3 + 3(2^2)(3) + 3(2)(3^2) + 3^3 = 8 + 36 + 54 + 27 = 125$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u8bb0\u4f4f\u201c\u7acb\u65b9\u516c\u5f0f\u662f\u5e73\u65b9\u52a0\u4e24\u500d\u4e58\u79ef\u518d\u52a0\u4e24\u4e2a\u5e73\u65b9\u7684\u4e58\u79ef\uff0c\u518d\u52a0\u7acb\u65b9\u201d\uff0c\u901a\u8fc7\u516c\u5f0f\u56fe\u793a\u5e2e\u52a9\u8bb0\u5fc6\u3002<\/p>\n
\n
7. \u5dee\u5e73\u65b9\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $a^2\u2212b^2=(a+b)(a\u2212b)a^2 – b^2 = (a + b)(a – b)<\/span>a^<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>b^<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>(<\/span>a<\/span>+<\/span><\/span>b<\/span>)<\/span>(<\/span>a<\/span>\u2212<\/span><\/span>b<\/span>)<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u5dee\u5e73\u65b9\u516c\u5f0f\u7528\u4e8e\u5feb\u901f\u8ba1\u7b97\u4e24\u4e2a\u5e73\u65b9\u5dee\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97 $9^2 – 4^2$
\n\u7b54\u6848\uff1a<\/strong>
\n$9^2 – 4^2 = (9 + 4)(9 – 4) = 13 \\$5 = 65$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u5c06\u5dee\u5e73\u65b9\u53d8\u6210\u4e24\u4e2a\u62ec\u53f7\u7684\u4e58\u6cd5\u5f62\u5f0f\uff0c\u4f8b\u5982 $a^2 – b^2$ \u5c31\u53ef\u4ee5\u53d8\u4e3a $(a + b)(a – b)$\u3002<\/p>\n
\n
8. \u5706\u7684\u9762\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $A=\u03c0r2A = \\pi r^2<\/span>A<\/span>=<\/span><\/span>\u03c0<\/span>r<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u5706\u7684\u9762\u79ef\u7b49\u4e8e\u5706\u7684\u534a\u5f84\u5e73\u65b9\u4e58\u4ee5\u5706\u5468\u7387 $\\pi$\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u534a\u5f84\u4e3a $3$ cm \u7684\u5706\u7684\u9762\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$A = \\pi \\times 3^2 = 9\\pi \\approx 28.27$ cm\u00b2<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u8bb0\u4f4f\u5706\u7684\u9762\u79ef\u516c\u5f0f\u662f\u201c\u534a\u5f84\u7684\u5e73\u65b9\u4e58 $\\pi$\u201d\uff0c\u800c\u5706\u7684\u5468\u957f\u662f\u201c2 \u500d\u534a\u5f84\u4e58 $\\pi$\u201d\u3002<\/p>\n
\n
9. \u5706\u7684\u5468\u957f\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $C=2\u03c0rC = 2\\pi r<\/span>C<\/span>=<\/span><\/span>2<\/span>\u03c0<\/span>r<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u5706\u7684\u5468\u957f\u7b49\u4e8e\u534a\u5f84\u4e58\u4ee5 2\uff0c\u518d\u4e58\u4ee5\u5706\u5468\u7387 $\\pi$\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u534a\u5f84\u4e3a $3$ cm \u7684\u5706\u7684\u5468\u957f\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$C = 2\\pi \\times 3 = 6\\pi \\approx 18.85$ cm<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u8bb0\u4f4f\u201c\u5706\u5468\u957f\u516c\u5f0f\u662f2\u500d\u534a\u5f84\u4e58 $\\pi$\u201d\u3002<\/p>\n
\n
10. \u77e9\u5f62\u7684\u9762\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $A=l\u00d7wA = l \\times w<\/span>A<\/span>=<\/span><\/span>l<\/span>\u00d7<\/span><\/span>w<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u77e9\u5f62\u7684\u9762\u79ef\u7b49\u4e8e\u957f\u4e58\u4ee5\u5bbd\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u957f\u4e3a $5$ cm\uff0c\u5bbd\u4e3a $3$ cm \u7684\u77e9\u5f62\u7684\u9762\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$A = 5 \\times 3 = 15$ cm\u00b2<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u77e9\u5f62\u7684\u9762\u79ef\u5c31\u662f\u957f\u4e58\u5bbd\uff0c\u53ef\u4ee5\u628a\u957f\u548c\u5bbd\u60f3\u8c61\u6210\u4e24\u4e2a\u76f8\u90bb\u7684\u8fb9\u3002<\/p>\n
\n
11. \u77e9\u5f62\u7684\u5468\u957f\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $P=2(l+w)P = 2(l + w)<\/span>P<\/span>=<\/span><\/span>2<\/span>(<\/span>l<\/span>+<\/span><\/span>w<\/span>)<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u77e9\u5f62\u7684\u5468\u957f\u7b49\u4e8e\u957f\u52a0\u5bbd\u7684\u548c\u518d\u4e58\u4ee5 2\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u957f\u4e3a $5$ cm\uff0c\u5bbd\u4e3a $3$ cm \u7684\u77e9\u5f62\u7684\u5468\u957f\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$P = 2(5 + 3) = 16$ cm<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u5468\u957f\u662f\u4e24\u500d\u7684\u957f\u548c\u5bbd\u4e4b\u548c\uff0c\u60f3\u8c61\u77e9\u5f62\u56db\u6761\u8fb9\u662f\u4e24\u8fb9\u957f\u548c\u4e24\u8fb9\u5bbd\u3002<\/p>\n
\n
12. \u6b63\u65b9\u5f62\u7684\u9762\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $A=a2A = a^2<\/span>A<\/span>=<\/span><\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u6b63\u65b9\u5f62\u7684\u9762\u79ef\u7b49\u4e8e\u8fb9\u957f\u7684\u5e73\u65b9\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u8fb9\u957f\u4e3a $4$ cm \u7684\u6b63\u65b9\u5f62\u7684\u9762\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$A = 4^2 = 16$ cm\u00b2<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u6b63\u65b9\u5f62\u7684\u9762\u79ef\u516c\u5f0f\u662f\u8fb9\u957f\u7684\u5e73\u65b9\uff0c\u56e0\u4e3a\u56db\u6761\u8fb9\u957f\u4e00\u6837\u3002<\/p>\n
\n
13. \u6b63\u65b9\u5f62\u7684\u5468\u957f\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $P=4aP = 4a<\/span>P<\/span>=<\/span><\/span>4<\/span>a<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u6b63\u65b9\u5f62\u7684\u5468\u957f\u7b49\u4e8e\u56db\u500d\u8fb9\u957f\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u8fb9\u957f\u4e3a $4$ cm \u7684\u6b63\u65b9\u5f62\u7684\u5468\u957f\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$P = 4 \\times 4 = 16$ cm<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u6b63\u65b9\u5f62\u56db\u6761\u8fb9\u76f8\u7b49\uff0c\u5468\u957f\u5c31\u662f\u8fb9\u957f\u4e58\u4ee5 4\u3002<\/p>\n
\n
14. \u68af\u5f62\u7684\u9762\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $A=(a+b)h2A = \\frac{(a + b)h}{2}<\/span>A<\/span>=<\/span><\/span>2<\/span><\/span>(<\/span>a<\/span>+<\/span>b<\/span>)<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u68af\u5f62\u7684\u9762\u79ef\u7b49\u4e8e\u4e24\u4e2a\u5e95\u8fb9\u7684\u548c\u4e58\u4ee5\u9ad8\u518d\u9664\u4ee5 2\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u5e95\u8fb9\u957f $6$ cm \u548c $4$ cm\uff0c\u9ad8\u4e3a $5$ cm \u7684\u68af\u5f62\u7684\u9762\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$A = \\frac{(6 + 4) \\times 5}{2} = 25$ cm\u00b2<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u68af\u5f62\u7684\u9762\u79ef\u662f\u5e95\u8fb9\u548c\u9ad8\u7684\u7ec4\u5408\uff0c\u8bb0\u4f4f\u516c\u5f0f\u4e2d\u4e24\u5e95\u8fb9\u52a0\u8d77\u6765\u540e\u518d\u9664\u4ee5 2\u3002<\/p>\n
15. \u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $A=bhA = bh<\/span>A<\/span>=<\/span><\/span>bh<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u7b49\u4e8e\u5e95\u8fb9\u957f\u4e58\u4ee5\u9ad8\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u5e95\u8fb9\u957f\u4e3a $5$ cm\uff0c\u9ad8\u4e3a $3$ cm \u7684\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$A = 5 \\times 3 = 15$ cm\u00b2<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u5c31\u662f\u5e95\u8fb9\u4e58\u4ee5\u9ad8\uff0c\u5e95\u8fb9\u548c\u9ad8\u5782\u76f4\u3002<\/p>\n
16. \u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $A=12\u00d7b\u00d7hA = \\frac{1}{2} \\times b \\times h<\/span>A<\/span>=<\/span><\/span>2<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>b<\/span>\u00d7<\/span><\/span>h<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u7b49\u4e8e\u5e95\u8fb9\u4e0e\u9ad8\u7684\u4e58\u79ef\u7684\u4e00\u534a\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u5e95\u8fb9\u4e3a $6$ cm\uff0c\u9ad8\u4e3a $4$ cm \u7684\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$A = \\frac{1}{2} \\times 6 \\times 4 = 12$ cm\u00b2<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u53ef\u4ee5\u60f3\u8c61\u6210\u4e00\u4e2a\u77e9\u5f62\u7684\u4e00\u534a\uff0c\u5e95\u8fb9\u548c\u9ad8\u76f8\u4ea4\u5f62\u6210\u76f4\u89d2\u3002<\/p>\n
\n
17. \u52fe\u80a1\u5b9a\u7406<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $a2+b2=c2a^2 + b^2 = c^2<\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>c<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u5728\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\uff0c\u4e24\u6761\u76f4\u89d2\u8fb9\u7684\u5e73\u65b9\u548c\u7b49\u4e8e\u659c\u8fb9\u7684\u5e73\u65b9\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u5df2\u77e5\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u4e24\u76f4\u89d2\u8fb9\u957f\u5206\u522b\u4e3a $3$ cm \u548c $4$ cm\uff0c\u6c42\u659c\u8fb9\u957f\u5ea6\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$3^2 + 4^2 = c^2 \\Rightarrow 9 + 16 = c^2 \\Rightarrow c = 5$ cm<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u52fe\u80a1\u5b9a\u7406\u662f\u8ba1\u7b97\u76f4\u89d2\u4e09\u89d2\u5f62\u659c\u8fb9\u7684\u4e00\u4e2a\u91cd\u8981\u5de5\u5177\uff0c\u8bb0\u4f4f\uff1a\u4e24\u76f4\u89d2\u8fb9\u7684\u5e73\u65b9\u548c\u7b49\u4e8e\u659c\u8fb9\u7684\u5e73\u65b9\u3002<\/p>\n
\n
18. \u957f\u65b9\u4f53\u7684\u4f53\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $V=l\u00d7w\u00d7hV = l \\times w \\times h<\/span>V<\/span>=<\/span><\/span>l<\/span>\u00d7<\/span><\/span>w<\/span>\u00d7<\/span><\/span>h<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u957f\u65b9\u4f53\u7684\u4f53\u79ef\u7b49\u4e8e\u957f\u3001\u5bbd\u3001\u9ad8\u7684\u4e58\u79ef\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u957f\u4e3a $4$ cm\uff0c\u5bbd\u4e3a $3$ cm\uff0c\u9ad8\u4e3a $2$ cm \u7684\u957f\u65b9\u4f53\u7684\u4f53\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$V = 4 \\times 3 \\times 2 = 24$ cm\u00b3<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u957f\u65b9\u4f53\u7684\u4f53\u79ef\u662f\u4e00\u4e2a\u7acb\u4f53\u7684\u6982\u5ff5\uff0c\u60f3\u8c61\u957f\u65b9\u4f53\u7684\u6bcf\u4e2a\u8fb9\u957f\u4e58\u8d77\u6765\u3002<\/p>\n
\n
19. \u7acb\u65b9\u4f53\u7684\u4f53\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $V=a3V = a^3<\/span>V<\/span>=<\/span><\/span>a<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u7acb\u65b9\u4f53\u7684\u4f53\u79ef\u7b49\u4e8e\u8fb9\u957f\u7684\u7acb\u65b9\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u8fb9\u957f\u4e3a $5$ cm \u7684\u7acb\u65b9\u4f53\u7684\u4f53\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$V = 5^3 = 125$ cm\u00b3<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u7acb\u65b9\u4f53\u7684\u4f53\u79ef\u662f\u8fb9\u957f\u7684\u7acb\u65b9\uff0c\u56e0\u4e3a\u5b83\u662f\u4e00\u4e2a\u5b8c\u5168\u5bf9\u79f0\u7684\u7acb\u4f53\u3002<\/p>\n
\n
20. \u5706\u67f1\u7684\u4f53\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $V=\u03c0r2hV = \\pi r^2 h<\/span>V<\/span>=<\/span><\/span>\u03c0<\/span>r<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u5706\u67f1\u7684\u4f53\u79ef\u7b49\u4e8e\u5706\u7684\u9762\u79ef\uff08$\\pi r^2$\uff09\u4e58\u4ee5\u5706\u67f1\u7684\u9ad8\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u534a\u5f84\u4e3a $3$ cm\uff0c\u9ad8\u4e3a $7$ cm \u7684\u5706\u67f1\u4f53\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$V = \\pi \\times 3^2 \\times 7 = 63\\pi \\approx 197.92$ cm\u00b3<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u5706\u67f1\u7684\u4f53\u79ef\u662f\u5e95\u9762\u79ef\uff08\u5706\u7684\u9762\u79ef\uff09\u4e58\u4ee5\u9ad8\uff0c\u8bb0\u4f4f\u516c\u5f0f\u4e2d\u7684 $\\pi r^2$ \u5c31\u662f\u5706\u7684\u9762\u79ef\u3002<\/p>\n
\n
21. \u5706\u9525\u7684\u4f53\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $V=13\u03c0r2hV = \\frac{1}{3} \\pi r^2 h<\/span>V<\/span>=<\/span><\/span>3<\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u03c0<\/span>r<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u5706\u9525\u7684\u4f53\u79ef\u662f\u5706\u67f1\u4f53\u79ef\u7684\u4e09\u5206\u4e4b\u4e00\uff0c\u5e95\u9762\u79ef\u4e58\u4ee5\u9ad8\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u534a\u5f84\u4e3a $3$ cm\uff0c\u9ad8\u4e3a $7$ cm \u7684\u5706\u9525\u4f53\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$V = \\frac{1}{3} \\pi \\times 3^2 \\times 7 = 21\\pi \\approx 65.97$ cm\u00b3<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u5706\u9525\u7684\u4f53\u79ef\u516c\u5f0f\u4e0e\u5706\u67f1\u7684\u76f8\u4f3c\uff0c\u53ea\u4e0d\u8fc7\u662f\u9664\u4ee5\u4e86 3\u3002\u53ef\u4ee5\u8bb0\u4f4f\u201c\u5706\u9525\u662f\u5706\u67f1\u7684\u4e09\u5206\u4e4b\u4e00\u201d\u3002<\/p>\n
\n
22. \u7403\u7684\u4f53\u79ef\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $V=43\u03c0r3V = \\frac{4}{3} \\pi r^3<\/span>V<\/span>=<\/span><\/span>3<\/span><\/span>4<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u03c0<\/span>r<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u7403\u7684\u4f53\u79ef\u7b49\u4e8e\u56db\u5206\u4e4b\u4e09\u4e58\u4ee5\u5706\u5468\u7387 $\\pi$ \u4e58\u4ee5\u534a\u5f84\u7684\u7acb\u65b9\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97\u534a\u5f84\u4e3a $5$ cm \u7684\u7403\u4f53\u79ef\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$V = \\frac{4}{3} \\pi \\times 5^3 = \\frac{4}{3} \\pi \\times 125 \\approx 523.6$ cm\u00b3<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u7403\u7684\u4f53\u79ef\u516c\u5f0f\u662f\u6700\u590d\u6742\u7684\uff0c\u53ef\u4ee5\u8bb0\u4f4f\u56db\u5206\u4e4b\u4e09\u4e58\u4ee5\u534a\u5f84\u7684\u7acb\u65b9\u518d\u4e58 $\\pi$\u3002<\/p>\n
\n
23. \u7b80\u5355\u767e\u5206\u6bd4\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $\u767e\u5206\u6bd4=\u90e8\u5206\u6570\u503c\u603b\u6570\u503c\u00d7100%\\text{\u767e\u5206\u6bd4} = \\frac{\\text{\u90e8\u5206\u6570\u503c}}{\\text{\u603b\u6570\u503c}} \\times 100\\%<\/span>\u767e\u5206\u6bd4<\/span><\/span>=<\/span><\/span>\u603b\u6570\u503c<\/span><\/span><\/span><\/span>\u90e8\u5206\u6570\u503c<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>100%<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u767e\u5206\u6bd4\u662f\u4e00\u4e2a\u6570\u503c\u5360\u603b\u6570\u503c\u7684\u767e\u5206\u6bd4\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u4e00\u4e2a\u73ed\u7ea7\u6709 $40$ \u4eba\uff0c$16$ \u4eba\u559c\u6b22\u770b\u7535\u5f71\uff0c\u6c42\u559c\u6b22\u770b\u7535\u5f71\u7684\u4eba\u5360\u73ed\u7ea7\u4eba\u6570\u7684\u767e\u5206\u6bd4\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n\u767e\u5206\u6bd4 = $\\frac{16}{40} \\times 100% = 40%$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u8ba1\u7b97\u767e\u5206\u6bd4\u65f6\uff0c\u5c06\u90e8\u5206\u6570\u503c\u4e0e\u603b\u6570\u503c\u7684\u6bd4\u503c\u4e58\u4ee5 100\uff0c\u5c31\u80fd\u5f97\u5230\u767e\u5206\u6bd4\u3002<\/p>\n
\n
24. \u5e73\u5747\u6570\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $\u5e73\u5747\u6570=\u6240\u6709\u6570\u503c\u4e4b\u548c\u6570\u503c\u4e2a\u6570\\text{\u5e73\u5747\u6570} = \\frac{\\text{\u6240\u6709\u6570\u503c\u4e4b\u548c}}{\\text{\u6570\u503c\u4e2a\u6570}}<\/span>\u5e73\u5747\u6570<\/span><\/span>=<\/span><\/span>\u6570\u503c\u4e2a\u6570<\/span><\/span><\/span><\/span>\u6240\u6709\u6570\u503c\u4e4b\u548c<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u5e73\u5747\u6570\u662f\u6240\u6709\u6570\u503c\u4e4b\u548c\u9664\u4ee5\u6570\u503c\u4e2a\u6570\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97 $2, 4, 6, 8, 10$ \u7684\u5e73\u5747\u6570\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n\u5e73\u5747\u6570 = $\\frac{2 + 4 + 6 + 8 + 10}{5} = 6$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u8ba1\u7b97\u5e73\u5747\u6570\u65f6\uff0c\u628a\u6240\u6709\u7684\u6570\u52a0\u8d77\u6765\uff0c\u518d\u9664\u4ee5\u4e2a\u6570\u5373\u53ef\u3002<\/p>\n
\n
25. \u4e24\u6570\u4e4b\u548c\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $(a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2<\/span>(<\/span>a<\/span>+<\/span><\/span>b<\/span>)2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>2<\/span>ab<\/span>+<\/span><\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u4e24\u6570\u4e4b\u548c\u7684\u5e73\u65b9\u7b49\u4e8e\u5404\u81ea\u7684\u5e73\u65b9\u52a0\u4e0a\u4e24\u500d\u4e58\u79ef\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u8ba1\u7b97 $(5 + 7)^2$
\n\u7b54\u6848\uff1a<\/strong>
\n$5^2 + 2(5)(7) + 7^2 = 25 + 70 + 49 = 144$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u8bb0\u4f4f\u201c\u5e73\u65b9\u52a0\u4e24\u500d\u4e58\u79ef\u52a0\u5e73\u65b9\u201d\u6765\u5e2e\u52a9\u8bb0\u5fc6\u3002<\/p>\n
\n
26. \u7b49\u5dee\u6570\u5217\u7684\u548c\u516c\u5f0f<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $Sn=n2\u00d7(a1+an)S_n = \\frac{n}{2} \\times (a_1 + a_n)<\/span>S<\/span>n<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>2<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span>a<\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>a<\/span>n<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u7b49\u5dee\u6570\u5217\u524d $n$ \u9879\u7684\u548c\u7b49\u4e8e\u9879\u6570\u4e58\u4ee5\u9996\u9879\u4e0e\u672b\u9879\u7684\u5e73\u5747\u503c\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u6c42\u7b49\u5dee\u6570\u5217 $1, 3, 5, 7, 9$ \u7684\u548c\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$S_5 = \\frac{5}{2} \\times (1 + 9) = \\frac{5}{2} \\times 10 = 25$<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u8bb0\u4f4f\u7b49\u5dee\u6570\u5217\u7684\u548c\u516c\u5f0f\uff0c\u901a\u8fc7\u9996\u9879\u548c\u672b\u9879\u7684\u5e73\u5747\u503c\u6765\u8ba1\u7b97\u3002<\/p>\n
\n
27. \u52fe\u80a1\u5b9a\u7406\u7684\u5e94\u7528<\/strong><\/h3>\n
\u516c\u5f0f\uff1a<\/strong>
\n $a2+b2=c2a^2 + b^2 = c^2<\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>c<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\n\u91ca\u4e49\uff1a<\/strong>\n\u52fe\u80a1\u5b9a\u7406\u5e94\u7528\u4e8e\u6c42\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u659c\u8fb9\u3002<\/p>\n$
\u4f8b\u9898\uff1a<\/strong>
\n\u5728\u4e00\u4e2a\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\uff0c\u76f4\u89d2\u8fb9\u5206\u522b\u4e3a $6$ cm \u548c $8$ cm\uff0c\u6c42\u659c\u8fb9\u957f\u5ea6\u3002
\n\u7b54\u6848\uff1a<\/strong>
\n$6^2 + 8^2 = c^2 \\Rightarrow 36 + 64 = c^2 \\Rightarrow c = 10$ cm<\/p>\n
\u5de7\u8bb0\u6280\u5de7\uff1a<\/strong>
\n\u8bb0\u4f4f\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u4e24\u6761\u76f4\u89d2\u8fb9\u5e73\u65b9\u548c\u7b49\u4e8e\u659c\u8fb9\u7684\u5e73\u65b9\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
1. \u52a0\u6cd5\u516c\u5f0f \u516c\u5f0f\uff1a a+b=ca + b = ca+b=c \u91ca\u4e49\uff1a \u52a0\u6cd5\u662f\u6700\u57fa\u7840\u7684\u8fd0\u7b97\uff0c\u7528\u6765\u6c42\u4e24\u4e2a\u6570\u7684\u548c\u3002 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[176],"tags":[],"content_type":[],"class_list":["post-12494","post","type-post","status-publish","format-standard","hentry","category-xxzfx"],"_links":{"self":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts\/12494","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12494"}],"version-history":[{"count":0,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts\/12494\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12494"},{"taxonomy":"content_type","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcontent_type&post=12494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}