Question

A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1.5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimetres ?

Answer 1

Given radius of cylinder =6cm,

radius of each sphere =1.5cm
raise in the level of oil=2cm

Volume of the raised oil in the cylinder = $\pi r^{2}h=\pi \times 6^2\times 2=72\pi c{m}^3$

Volume of 1 sphere

$=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\pi (1.5{)}^3=\frac{9\pi }{2}c{m}^3$

Let the number of sphere which when immersed in the oil raise the level by 2cm be n.

Then,

Volume of n spheres = $=n\times \frac{9\pi }{2}c{m}^3$ =Volume of the raised oil

$=>n\times \frac{9\pi }{2}=72\pi$

$=>n=\frac{72\times 2}{9}=16$

Hence the required number of spheres=16