Question

A sphere of diameter $6cm$ is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is $12cm$. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

Answer 1

sphere diameter $=6cm$

radius of sphere $=\frac{d}{2}=3cm=R$

$\to$ diameter of cylinder $d=12cm$

radius of cylinder $=\frac{12}{2}=6cm=R$

$\to$ sphere is submerge in cylinder, so,

volume of the water required in the vessel

$=$ volume of sphere

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

$\therefore h=\frac{4}{3}\times r^3\times \frac{1}{R^2}$

$=\frac{4}{3}\times (3{)}^3\times \frac{1}{(6{)}^2}$

$\therefore h=1cm$