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?

 Given:

A cylindrical jar of radius $6\ cm$ contains oil. Iron spheres each of radius $1.5\ cm$ 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 $(r) = 6\ cm$

Level of oil in the jar $(h) = 2\ cm$

Therefore,

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

$=\pi(6)^{2} \times 2$

$=72 \pi \mathrm{cm}^{3}$

Radius of the iron sphere $=1.5 \mathrm{~cm}$

Volume of one sphere $=\frac{4}{3} \pi(1.5)^{3} \mathrm{~cm}^{3}$

$=\frac{4}{3} \pi \times \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2}$

$=\frac{9}{2} \pi \mathrm{cm}^{3}$

Therefore,

Number of spheres that are necessary $=\frac{72 \pi}{\frac{9}{2} \pi}$

$=\frac{72 \times 2}{9}$

$=16$

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Updated on: 10-Oct-2022

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