A cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water level in the tank.

Given,

Diameter of cylindrical bucket = 28 cm

Radius (r) = $\dfrac{\text{Diameter}}{2} = \dfrac{28}{2}$ = 14 cm.

Height (H) = 72 cm.

Length of rectangular tank (l) = 66 cm

Breadth of rectangular tank (b) = 28 cm.

Let height of water be h cm in the rectangular tank.

Since, water is emptied into a rectangular tank from cylindrical bucket,

∴ Volume of cylindrical bucket = Volume of water in rectangular tank

$\Rightarrow πr^2H = l × b × h \\[1em] \Rightarrow h = \dfrac{πr^2H}{lb} \\[1em] \Rightarrow h = \dfrac{\dfrac{22}{7} \times 14^2 \times 72}{66 \times 28} \\[1em] \Rightarrow h = \dfrac{22 \times 196 \times 72}{7 \times 66 \times 28} \\[1em] \Rightarrow h = \dfrac{7 \times 72}{7 \times 3} \\[1em] \Rightarrow h = 24\text{ cm}.$

Hence, height of water level in rectangular tank = 24 cm.