# A vessel in the form of a hemispherical bowl is full of water.

Question:

A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.

Solution:

Given that

Volume of water in the hemispherical bowl = Volume of water in the cylinder

Let h be the height to which water rises in the cylinder

Inner radii of the bowl = r1 = 3.5 cm

Inner radii of the bowl = r2 = 7 cm

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

$\mathrm{h}=\frac{2 \mathrm{r}_{1}^{3}}{3 \mathrm{r}_{2}^{2}}$

$h=\frac{2(3.5)^{3}}{3\left(7^{2}\right)}$

h = 7/12 cm