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  • The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is: (A) 10 : 17 (B) 20 : 27 (C) 17 : 27 (D) 20 : 37

The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is:

(A) 10 : 17

(B) 20 : 27

(C) 17 : 27

(D) 20 : 37

Answers (1)

Answer (B)

We know that volume of a cylinder is given as \pi r^{2}h

Where r is the radius of its base and h is the height.

 Now it is given that ratio of Radius =r_{1}:r_{2}=2:3

And, Ratio of Heights =h_{1}:h_{2}=5:3

So, Ratio of volumes,

\pi r_{1}^{2}h_{1}:\pi r_{2}^{2}h_{2}

=\frac{\pi r_{1}^{2}h_{1}}{\pi r_{2}^{2}h_{2}}

=\left ( \frac{r_{1}}{r_{2}} \right )^{2}\left ( \frac{h_{1}}{h_{2}} \right )

=\left ( \frac{2}{3} \right )^{2}\left ( \frac{5}{3} \right )

=\left ( \frac{4}{9} \right )\left ( \frac{5}{3} \right )

= \frac{20}{27}

= 20:27

So, option (B) is the correct answer.

 

Posted by

infoexpert23

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