Question

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

Answer 1

Dimensions of the metal cuboid are

Length $=l=22$cm

Breadth $=b=15$cm

Height $=h=7.5$cm

Height of the cylinder $\left(H\right)=14$cm

Let the radius of the cylinder be $r$ cm

Volume of cuboid $=$ Volume of cylinder

$l\times b\times h=\pi r^{2}h$

$\Rightarrow 22\times 15\times 7.5=\frac{22}{7}\cdot r^2\cdot 14$

$\Rightarrow 2475=\mathrm{22.2.}{r}^2$

$\Rightarrow r^2=\frac{2475}{22.2}$

$\Rightarrow r^2=56.25$

$\Rightarrow r=\sqrt{56.25}$

$\Rightarrow r=7.5$

$\therefore$ Radius $=r=7.5$cm.