找出圆锥体表面积并不那么难,但有些问题也比较刁钻,需要巧妙的思维和勤奋的练习才能解出来。下面介绍一些步骤,教你如何解各种关于圆锥体表面积的问题。
步骤
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/6e\/Find-the-Surface-Area-of-Cones-Step-1.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-1.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/6e\/Find-the-Surface-Area-of-Cones-Step-1.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
1
先要找出底部圆的半径。如果得到了直径,除以2即可。如果有斜高和垂直高,则用勾股定理接触半径(下面的“小提示”有讲)。
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/b\/b7\/Find-the-Surface-Area-of-Cones-Step-2.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/b\/b7\/Find-the-Surface-Area-of-Cones-Step-2.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
2
在旁边写下半径,要标出来以便找到,因为后面好几个计算步骤需要用到。
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/5\/5d\/Find-the-Surface-Area-of-Cones-Step-3.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/5\/5d\/Find-the-Surface-Area-of-Cones-Step-3.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
3
半径平方乘以π,求出底部圆的面积。
- 如果需要你求“准确值”,则需要写下“π”,比如半径为3的圆,其面积是9π。
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/f6\/Find-the-Surface-Area-of-Cones-Step-3Bullet1.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-3Bullet1.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/f6\/Find-the-Surface-Area-of-Cones-Step-3Bullet1.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-3Bullet1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
- 否则就用3.14这个粗略值,或者用计算器的π按钮,得出精确到小数值的面积值。
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/d2\/Find-the-Surface-Area-of-Cones-Step-3Bullet2.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-3Bullet2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/d2\/Find-the-Surface-Area-of-Cones-Step-3Bullet2.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-3Bullet2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
- 你可以四舍五入,不过目前答案的小数点之后至少要留3位数字。
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/f6\/409595-3b2b1.JPG\/v4-460px-409595-3b2b1.JPG","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/f6\/409595-3b2b1.JPG\/v4-728px-409595-3b2b1.JPG","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/37\/Find-the-Surface-Area-of-Cones-Step-4.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-4.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/37\/Find-the-Surface-Area-of-Cones-Step-4.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
4
答案写在一边,用“底面积”标出。
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/16\/Find-the-Surface-Area-of-Cones-Step-5.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-5.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/16\/Find-the-Surface-Area-of-Cones-Step-5.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-5.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
5
找出圆锥的斜高。表示斜面上的高,而不是定点到底面圆的高。
- 半径、垂直高度(定点到底面)和斜高成勾股定理关系。下面的小提示会提到。
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/9\/9d\/Find-the-Surface-Area-of-Cones-Step-5Bullet1.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-5Bullet1.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/9\/9d\/Find-the-Surface-Area-of-Cones-Step-5Bullet1.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-5Bullet1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/f8\/Find-the-Surface-Area-of-Cones-Step-6.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-6.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/f8\/Find-the-Surface-Area-of-Cones-Step-6.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-6.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
6
用斜高乘以半径再乘π。这里重复一次,“准确值”需要你把π写出来,保留在那儿不动,如果不需要准确值,就用3.14求含有小数部分的粗略计算值。
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/7\/7d\/Find-the-Surface-Area-of-Cones-Step-7.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-7.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/7\/7d\/Find-the-Surface-Area-of-Cones-Step-7.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-7.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
7
再写在一边,这里标成“侧面积”,之后好找。
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/0\/00\/Find-the-Surface-Area-of-Cones-Step-8.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-8.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/0\/00\/Find-the-Surface-Area-of-Cones-Step-8.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-8.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
8用第四步的底面积加上上一步的侧面积
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/8\/8c\/Find-the-Surface-Area-of-Cones-Step-9.jpg\/v4-460px-Find-the-Surface-Area-of-Cones-Step-9.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/8\/8c\/Find-the-Surface-Area-of-Cones-Step-9.jpg\/v4-728px-Find-the-Surface-Area-of-Cones-Step-9.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
9
如果需要就四舍五入,化简一下,得到最终答案。
小提示
- 通用凑整规则:任何小于20的答案,都至少要有2位小数数字。20到100间的答案只要1位小数,大于100就不用小数。
- 勾股定理可以用在圆锥体的斜高、半径和垂直高上,斜高作为“直角三角形”的斜边部分。 (半径)2 + (垂直高)2 = (斜面高)2
警告