# A cylinder of radius 12 cm contains water to a depth of 20 cm.

Question:

A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball. (Use = 227).

Solution:

Given that:

Radius of the cylinder = 12cm = r1

Raised in raised = 6.75 cm = r2

Volume of water raised = Volume of the sphere

$=\pi r_{1}^{2} h=\frac{4}{3} \pi r_{2}^{3}$

$=12 \times 12 \times 6.75=\frac{4}{3} \mathrm{r}_{2}^{3}$

$=r_{2}^{3}=\frac{12 \times 12 \times 6.75 \times 3}{4}$

$=\mathrm{r}_{2}^{3}=729$

= r2 = 9 cm

Radius of the sphere is 9 cm