Question

The radii of two cylinders are in the ratio 2 : 3 and their curved surface areas are in the ratio 5 : 3. What is the ratio of their volumes?




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Answer 1

Answer:

20 : 27 is the answer

Step-by-step explanation:

Given:- radii of two cylinders are in the ratio 2 : 3

            their curved surface areas are in the ratio 5 : 3

Find:- the ratio of their volumes?

Solution:-

let the radii of the two cylinders be $r_{1}$ and $r_{2}$ and height of the two cylinders be $h_{1}$ and $h_{2}$ .

In Given,

$\frac{r_{1} }{r_2} = \frac{2}{3}$ and $\frac{h_1}{h_2} =\frac{5}{3}$

∴the ratio of their volumes= $\frac{\pi x_1^{2}h_1}{\pi x_2^{2}h_2} =(\frac{r_1}{r_2} )^2 (\frac{h_1}{h_2} )$

$(\frac{2}{3}) ^2(\frac{5}{3} ) = \frac{4}{9}*\frac{5}{3} =\frac{20}{27}$

hence, the ratio of the volume is $\frac{20}{27}$

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