Question

The radius of a cylindrical vessel is $7cm$ and its height is $12cm$. $\frac{2}{3}$ of the vessel is filled with water. A sphere having radius $6cm$ is dropped into the water. Find the volume of the water that will come out of the vessel.

• A. $196\pi$ ${cm}^3$
• B. $92\pi$ ${cm}^3$
• C. $288\pi$ ${cm}^3$
• D. $588\pi$ ${cm}^3$

Answer 1

The correct option is B $92\pi$ ${cm}^3$

Radius of cylindrical vessel $=7cm$ and height $=12cm$
$\therefore$ Volume $=\pi r^{2}h$
$=588\pi$
Volume of vessel filled with water $=\frac{2}{3}\times 588\pi =392\pi$
Volume of sphere $=\frac{4}{3}\times \pi \times 216=288\pi$
$\therefore$ Water spilled outside
$=(392+288)\pi -588\pi =92\pi c{m}^3$