Question

The radius of two cylinders are in the ratio of 3:2 and their heights are in the ratio 3:7. The ratio of their volumes is :

A) 4:7 B) 7:4 C) 28:27 D) 27:28

Answer 1

Given :

• The radius of two cylinders are in the ratio of 3:2.
• Their heights are in the ratio 3:7.

To find :

• TH ratio of their volumes =?

Step-by-step explanation :

Let radius of first cylinder = $\tt r_1$

and height of the first cylinder =$\tt h_1$

∴ Volume of first cylinder,$\tt V_1 =\pi r^2_1h_1$

Let radius of second cylinder =$\tt r_2$

& height of second cylinder =$\tt h_2$

∴ Volume of second cylinder,$\tt V_2 =\pi r^2_2 h_2$

According to the question,

$:\implies \tt \dfrac{V_1}{V_2} = \dfrac{\pi r^2_1h_1}{\pi r^2_2 h_2}$

$:\implies\tt \dfrac{V_1}{V_2} = \dfrac{r^2_1h_1}{r^2_2 h_2}$

$:\implies\tt \dfrac{V_1}{V_2} = \dfrac{3^2_1 3_1}{2^2_2 7_2}$

$:\implies\tt \dfrac{V_1}{V_2} = \dfrac{9 \times 3}{4 \times 7}$

$:\implies\tt \dfrac{V_1}{V_2} = \dfrac{{27}}{{28}}$

Therefore, The ratio of their volumes is, 27 : 28.

Hence, Option d). 27:28 is the correct option.