Question

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

Answer 1

Given a metal cuboid of dimension length 22 cm breadth 15 cm and height is 7.5 cm

Then volume of cuboid $=22\times 15\times 7.5=2475c{m}^3$

If we melt this cuboid and cast in the cylinder of height $14cm$

Then the volume of cuboid =volume of cylinder

Let $r$ is a radius of a cylinder

Then volume of cylinder =$\pi r^{2}h=\frac{22}{7}\times r^2\times 14$

$\therefore \frac{22}{7}\times r^2\times 14=2475$

$\Rightarrow r^2=\frac{2475\times 7}{22\times 14}=56.25$

$\Rightarrow r=7.5cm$