AMC8 1992

AMC8 1992 · Q16

AMC8 1992 · Q16. It mainly tests 3D geometry (volume).

Which cylinder has twice the volume of the cylinder shown to the right?

哪个圆柱体的体积是右侧所示圆柱体的两倍？

(A)

(B)

(C)

(D)

(E) None of the above 以上皆非

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Cylinder (B) can be obtained by stacking one copy of the given cylinder on top of another. The formula for the volume of a cylinder with radius r and height h is V = πr²h. Use this to show that none of the other cylinders has twice the volume of the given cylinder: Cylinder | Volume Given: | π × 10² × 5 = 500π (A): | π × 20² × 5 = 2000π (C): | π × 5² × 20 = 500π (D): | π × 20² × 10 = 4000π Note. If the radius remains the same and the height is doubled, then the volume will double as in (B). Doubling the radius while the height remains the same will multiply the volume by 4, as in (A).

答案 (B)：圆柱 (B) 可由两个给定圆柱叠加得到。圆柱体积公式为 V = πr²h。用此显示其他圆柱体积不是给定圆柱的两倍：圆柱 | 体积给定 | π × 10² × 5 = 500π (A) | π × 20² × 5 = 2000π (C) | π × 5² × 20 = 500π (D) | π × 20² × 10 = 4000π 注：半径不变高度加倍则体积加倍，如(B)。半径加倍高度不变则体积乘4，如(A)。

Topics

GE.013 3D geometry (volume)