Question

A metal cuboid of dimension $22cm\times 15cm\times 7.5cm$ was melted and cast into a cylinder of height $14cm$ . What is the radius of the cylinder?

Answer 1

Dimensions of the cuboid $=$$22cm\times 15cm\times 7.5cm$

The volume of the cuboid $$\begin{gathered} =l\times b\times h \\ =22cm\times 15cm\times 7.5cm \\ =2475c{m}^3 \end{gathered}$$

The volume of a cylinder $$\begin{gathered} =\pi r^{2}h \\ =\frac{22}{7}\times r^2\times 14 \\ =r^2\times 44=44r^2 \end{gathered}$$

Given that cuboid was melted into a cylinder, so the volume of the cuboid is equal to the volume of a cylinder.

So, $$\begin{gathered} 44r^2=2475 \\ {r}^2=\frac{2475}{44} \\ {r}^2=56.25 \\ r=\sqrt{56.25} \\ r=7.5cm \end{gathered}$$

Hence, the radius of the cylinder is equal to $7.5cm$.