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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