Question

The given figure shows a solid sphere and a closed cylindrical container, both having the same height and same radii. The volume of air left in the cylinder is:

Options

• 6πr³

• 3/2πr³

• 2/3πr³

• 4πr³

Answer 1

2/3πr³

Explanation:

From figure,

Radius of sphere = Radius of cylinder = r

Height of cylinder (h) = 2r

Volume of air left = Volume of cylinder − Volume of sphere

\[{} = \pi r^2 h - \frac{4}{3}\, \pi r^3\]

\[{} = \pi r^2 \cdot 2r - \frac{4}{3}\, \pi r^3\]

\[{} = 2\pi r^3 - \frac{4}{3}\, \pi r^3\]

\[{} = \frac{6\pi r^3 - 4\pi r^3}{3}\]

\[{} = \frac{2\pi r^3}{3}\]

\[{} = \frac{2}{3}\, \pi r^3\]