Question

A cylindrical jar of radius $12cm$ contains oil. Iron spheres each of radius $3cm$ are immersed in the oil. How many such spheres are needed to raise the oil by $4cm$?

• A. 16
• B. 8
• C. 10
• D. 32

Answer 1

The correct option is A

16

Note that,
Volume of the cylinder with height $4cm$ = $n\times$ Volume of one iron sphere, where $n$ is the required number of iron spheres.
Let $R$ and $r$ be the radii of the cylindrical jar and the iron sphere respectively. i.e., $R=12cmandr=3cm$
Then we have,$\pi R^{2}h=n\times \frac{4}{3}\pi \times r^3$
$⟹\pi {12}^2\times 4=n\times \frac{4}{3}\pi \times 3^3$
$⟹n=16$
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