Question 84

The ratio of radii of two cylinders is 2 : 3. Their heights are in the ratio 5 : 3. If one cylinder has a volume of 160 cubic units, what is the volume of the other cylinder?

Solution

We know that Volume of a cylinder= π×r×r×h

Let the radius and height of cylinder one and two be r1,r2 and h1,h2 respectively. Volumes be v1 and v2 respectively.

Given r1:r2 = 2:3

h1:h2 = 5:3

v1 = 160

Therefore $$ \frac{v1}{v2} = \frac {\pi r1^2 h1}{\pi r2^2 h2} $$

$$ \frac{160}{v2} = \frac {\pi 2^2 5}{\pi 3^2 3} $$

=> $$ v2 = \frac {160 \times 3^2 \times 3} {2^2\times5}$$

=>$$ v2 = 216 cubic units $$

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