Question

If a solid cone of volume $27\pi c{m}^3$ is kept inside a hollow cylinder whose radius and height are that of the cone, then, the volume of water needed to fill the empty space is

• A. $3\pi c{m}^3$
• B. $18\pi c{m}^3$
• C. $54\pi c{m}^3$
• D. $81\pi c{m}^3$

Answer 1

The correct option is C $54\pi c{m}^3$

Volume of cone $=\frac{1}{3}\pi r^{2}h$

Volume of cylinder$=\pi r^{2}h$

Empty space $=$Volume of cylinder$-$Volume of cone

$=\pi r^{2}h-\frac{1}{3}\pi r^{2}h$

$⟹$ Empty space $=\frac{2}{3}\pi r^2$

Empty space volume is $\frac{2}{3}$ times of cylinder$=2$ times volume of cone

$⟹$ Volume of water required$=27\pi \times 2=54\pi c{m}^3$