# A cylindrical jar of radius 6 cm contains oil.

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?

Solution:

The radius of the cylindrical jar is 6cm. The volume of the oil of height 2cm contained in the jar is

$V=\pi \times(6)^{2} \times 2$ cubic $\mathrm{cm}$

The radius of each small sphere is 1.5cm. Therefore, the volume of each small sphere is

$V_{1}=\frac{4}{3} \times \pi \times(1.5)^{3}$ cubic $\mathrm{cm}$

Since, the volume of the raised water is same as the sum of the volumes of the immersed iron spheres, we have the number of immersed sphere is

$\frac{V}{V_{1}}=\frac{\pi \times(6)^{2} \times 2}{\frac{4}{3} \times \pi \times(1.5)^{3}}$

$=\frac{3 \times 36 \times 2 \times 1000}{4 \times 15 \times 15 \times 15}$

$=16$

Therefore, the number of iron spheres is 16