Question

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

Answer 1

Suppose that the radius of the ball is r cm.
Radius of the cylindrical tub =12 cm
Depth of the tub= 20 cm
Now, volume of the ball = volume of water raised in the cylinder
$$\begin{gathered} \Rightarrow \frac{4}{3}\mathrm{\pi }{r}^3=\mathrm{\pi }\times {12}^2\times 6.75 \\ \Rightarrow r^3=\frac{144\times 6.75\times 3}{4}=36\times 6.5\times 3=729 \\ \Rightarrow r=9\mathrm{cm} \end{gathered}$$

∴ The radius of the ball is 9 cm.