A measuring jar of internal diameter 10 cm is partially filled with water. Four equal spherical balls of diameter 2 cm each are dropped in it and they sink down in water completely. What will be the change in the level of water in the jar?
Given that,
Diameter of jar = 10 cm
Radius of jar = 5 cm
Let the level of water be raised by h
Diameter of the spherical bowl = 2 cm
Radius of the ball = 1 cm
Volume of jar = 4 (Volume of spherical ball)
$\pi r_{1}^{2} h=4\left(\frac{4}{3} \pi r_{2}^{3}\right)$
$r_{1}^{2} h=4\left(\frac{4}{3} r_{2}^{3}\right)$
$5 \times 5 \times \mathrm{h}=4 \times \frac{4}{3} \mathrm{r}_{2}^{3}$
$5 \times 5 \times \mathrm{h}=4 \times \frac{4}{3} \times 1 \times 1 \times 1$
$h=\frac{4 \times 4 \times 1}{3 \times 5 \times 5}$
Height of water in jar = 16/75 cm