Question

The diameters of two cylinders are in the ratio of 2:1 and their volumes are equal. The ratio of their heights will be _________.

• A. 1:6
• B. 1:2
• C. 1:4
• D. 3:4

Answer 1

Answer: (C)

1:4

Let the diameter of the given two cylinders are $2x$ and $x$,

so the radius of these cylinders are $x$ and $0.5x$ respectively.

Let the height of these cylinders are $h_1$ and $h_2$ respectively.

Given $\pi x^2{h}_1=\pi (0.5x{)}^2{h}_2$

$\therefore \frac{h_1}{h_2}=\frac{(0.5{)}^2}{1}=\frac{1}{4}$

$1:4.$