Question 68

The radii of a sphere and a right circular cylinder are equal and their curved surface areas are also equal. The ratio of their volumes is

Solution

Curved surface area of sphere = $$4 \pi r^{2}$$

Curved surface area of a right circular cylinder = $$2 \pi rh$$

As per the given question these two are equal,

$$4 \pi r^{2}$$ = $$2 \pi rh$$

h = 2r ........(1)

Required ratio,

$$\frac{4}{3} \pi r^{3}$$ : $$\pi r^{2} h$$

4r : 3h

Substitute (1) in the above equation

4r : 3(2r) = 2:3

Hence, option B is the correct answer.

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