三棱柱公式的体积
棱镜是具有两个相同端的三维立体图形。它由平坦的侧面、相似的底座和相等的横截面组成。它的面是没有底的平行四边形或矩形。这种具有三个矩形面和两个平行三角形底面的棱镜称为三角棱镜。三角形底座由相互平行的侧面连接。
三棱柱公式的体积
三棱柱的体积定义为它内部的空间或被它填充的空间。知道三棱柱的底面积和高度是计算其体积所需的全部内容。三棱柱的体积等于底面积与棱柱高的乘积,也称为棱柱的长度。三棱柱的底面积等于三棱柱的底面和高的乘积的一半。
公式
V = (1/2) × b × h × l
where,
b is the triangular base,
h is the altitude of the prism,
l is the length of prism.
示例问题
问题 1. 求一个三棱柱的体积,如果它的底是 6 厘米,高是 8 厘米,长是 12 厘米。
解决方案:
We have, b = 6, h = 8 and l = 12.
Using the formula we have,
V = (1/2) × b × h × l
= (1/2) × 6 × 8 × 12
= 3 × 8 × 12
= 288 cu. cm
问题 2. 求一个三棱柱的体积,如果它的底是 5 厘米,高是 7 厘米,长是 8 厘米。
解决方案:
We have, b = 5, h = 7 and l = 8.
Using the formula we have,
V = (1/2) × b × h × l
= (1/2) × 5 × 7 × 8
= 5 × 7 × 4
= 140 cu. cm
问题 3. 求底边为 6 厘米,高为 9 厘米,体积为 98 立方的三棱柱的长度。厘米。
解决方案:
We have, b = 6, h = 9 and V = 98.
Using the formula we have,
V = (1/2) × b × h × l
=> 98 = (1/2) × 6 × 9 × l
=> 196 = 27l
=> l = 196/27
=> l = 7.25 cm
问题 4. 求底边为 8 厘米、长度为 14 厘米、体积为 504 立方的三棱柱的高度。厘米。
解决方案:
We have, b = 8, l = 14 and V = 504.
Using the formula we have,
V = (1/2) × b × h × l
=> 504 = (1/2) × 8 × h × 14
=> 504 = 56h
=> h = 504/56
=> h = 9 cm
问题 5. 求长 18 厘米、高 10 厘米、体积 450 立方的三棱柱底面积。厘米。
解决方案:
We have, l = 18, h = 10 and V = 450.
Using the formula for volume we have,
V = (1/2) × b × h × l
=> 450 = (1/2) × b × 10 × 18
=> 450 = 90b
=> b = 450/90
=> b = 5 cm
Hence, the area of triangular base is,
A = (1/2) × b × h
= (1/2) × 5 × 10
= 25 sq. cm