Question

A cylindrical bucket with base radius 15 cm is filled with water up to a height of 20 cm. A heavy iron spherical ball of radius 9 cm is dropped into the bucket to submerge completely in the water. Find the increase in the level of water.

Answer 1

Let h cm be the increase in the level of water.
Radius of the cylindrical bucket = 15 cm
Height up to which water is being filled = 20 cm
Radius of the spherical ball = 9 cm
Now, volume of the sphere = increased in volume of the cylinder
$$\begin{gathered} \Rightarrow \frac{4}{3}\mathrm{\pi }\times 9^3=\mathrm{\pi }\times {15}^2\times h \\ \Rightarrow h=\frac{4\times 729}{3\times 15\times 15}=\frac{4\times 27}{25}=4.32\mathrm{cm} \end{gathered}$$

∴ The increase in the level of water is 4.32 cm.