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?

Correct option is C

Given:

Ratio of radii = 2:3, ratio of heights = 5:3, volume of first cylinder = 160 cubic units.

Formula Used:

Volume of a cylinder = πr²h

Solution:

Let the radii of the two cylinders be 2x and 3x, and the heights be 5y and 3y.

Volume of the first cylinder = π(2x)²(5y)

20π$$x^2y$$​= 160.

​$$x^2y = \frac{160}{20\pi}$$​​

Volume of the second cylinder = π(3x)²(3y) = 27 $$\pi x^2y$$ = $$27 \times \frac{160}{20 \pi}$$ = 216 cubic units​