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

Given:

A cylindrical jar of radius \( 6 \mathrm{~cm} \) contains oil. Iron spheres each of radius \( 1.5 \mathrm{~cm} \) are immersed in the oil.

To do:

We have to find the number of spheres necessary to raise the level of the oil by two centimetres.

Solution:

Radius of the cylindrical jar $r=6 \mathrm{~cm}$

Rise(height) of the level of oil $=2 \mathrm{~cm}$

This implies,

Volume of oil in the jar $=\pi r^{2} h$

$=\frac{22}{7} \times(6)^{2} \times 2$

$=\frac{36 \times 44}{7} \mathrm{~cm}^{3}$

Radius of each iron sphere $r_{1}=1.5 \mathrm{~cm}$

This implies,

Volume of each sphere $=\frac{4}{3} \pi r_{1}^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times(1.5)^{3}$

$=\frac{88}{21} \times(\frac{3}{2})^{3}$

$=\frac{88}{21} \times \frac{27}{8}$

$=\frac{99}{7} \mathrm{~cm}^{3}$

Number of spheres necessary to raise the level of the oil by two centimetres $=$ Volume of oil in the jar $\div$ Volume of each sphere

$=\frac{36 \times 44}{7} \div \frac{99}{7}$

$=\frac{36 \times 44}{7} \times \frac{7}{99}$

$=16$

The number of spheres necessary to raise the level of the oil by two centimetres is $16$.

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Updated on: 10-Oct-2022

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