Question

A cylindrical box of radius 5 cm contains 10 solid spherical balls, each of radius 5 cm. If the top most ball touches the upper cover of the box, then the volume of empty space in the box is:

Accepted Answer

A. Height of the cylinder = $10 	imes 2r = 10 	imes 10 = 100$ cm. Volume of cylinder = $\pi r^2 h = \pi (5^2) (100) = 2500\pi$ cm$^3$. Volume of 10 spherical balls = $10 	imes \frac{4}{3}\pi (5^3) = \frac{5000}{3}\pi$ cm$^3$. Volume of empty space = $2500\pi - \frac{5000}{3}\pi = \frac{2500}{3}\pi$ cm$^3$.

Volume of Empty Space in Cylinder

Explanation

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