Question

A cylindrical bucket, 28 cm in diameter and 72 cm and 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.

Answer 1

Given: Diameter of the cylindrical bucket = 28 cm
i.e., radius = 14 cm
Height of the cylindrical bucket, h₁ = 72 cm
Length of the rectangular tank, l = 66 cm
Breadth of the rectangular tank, b = 28 cm
Let the height of the rectangular tank be h cm.
The water from the cylindrical bucket is emptied into the rectangular tank.
i.e., volume of the bucket = volume of the tank
$$\begin{gathered} \Rightarrow \mathrm{\pi }{r}^{\mathit{2}}{h}_{\mathit{1}}=l\mathit{\times }b\mathit{\times }h \\ \Rightarrow \frac{22}{7}\times {14}^2\times 72=66\times 28\times h \\ \Rightarrow h=\frac{22\times 14\times 2\times 72}{66\times 28}=24\mathrm{cm} \end{gathered}$$

∴ Height of the rectangular tank = 24 cm