Question

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

Answer 1

Suppose $x$ iron spheres are required to raise the level of the oil by two cm. then, volume of $x$ iron spheres$=$ volume of oil raised
$\Rightarrow x\times \frac{4}{3}\pi \times {\left(1.5\right)}^3=\pi \times 6^2\times 2\Rightarrow x\times \frac{4}{3}\pi {\left(\frac{3}{2}\right)}^2=72\pi \Rightarrow x=16$