Question

A solid sphere of diameter $6cm$ is dropped into a right circular cylindrical vessel with diameter $12cm$, which partly filled with water. If the sphere is completely submerged in water, how much does the water level in the cylindrical vessel increase?

Answer 1

Diameter of the sphere (d)$=6cm$

Radius of the sphere (r) $=\frac{d}{2}=\frac{6}{2}=3cm$

Diameter of the cylinder vessel (D) $=12cm$

Radius of the cylinder vessel (R)$=\frac{12}{2}=6cm$

Level of water raised $=4cm$

According to problem given :

Volume of water raised in the vessel $=$ volume of the sphere

$\Rightarrow \pi R^{2}h=\frac{4}{3}\pi r^2$

$\Rightarrow h=\frac{(4\times r^3)}{3\times R^2}$

$=\frac{4\times 3\times 3\times 3}{3\times 6\times 6}$

$\Rightarrow h=1cm$

Therefore level of water raised $=1cm.$

Hence, the answer is $1.$