Question

The radii of the bases of two cylinders are in the ratio 1:2 respectively and their heights are in the ratio 2:1 respectively. Find the ratio of their volumes

Answer 1

Let radius of first cylinder is $r_1$ and radius of 2nd cylinder is $r_2$.

height of first cylinder is $h_1$ and height of 2nd cylinder is $h_2$.

it is given that,
$\frac{r_1}{r_2}=\frac{1}{2}$

$\frac{h_1}{h_2}=\frac{2}{1}$

volume of cylinder = πr²h
e.g., volume of cylinder is directly proportional to square of radius and height .

so, $\frac{\textbf{volume of 1st cylinder}}{\textbf{volume of 2nd cylinder}}=\frac{r_1^2h_1}{r_2^2h_2}$

= $\left(\frac{r_1}{r_2}\right)^2\left(\frac{h_1}{h_2}\right)$

= (1/2)² × (2/1)

= 1/4 × 2/1 = 1/2 or 1 : 2