Question

The base radius of an iron cylinder is 18 cm and its height is 30 cm. It is melted and recast into a cylinder of base 12 cm. What is the height of the new cylinder?

Answer 1

Given

Radius of first cylinder $\left(r_1\right)=18\text{cm}$

Height of first cylinder $\left(h_1\right)=30\text{cm}$

Base radius of new cylinder $\left(r_2\right)=12\text{cm}$

Height of new cylinder $\left(h_2\right)=?$

Since the first cylinder is melted and recast into new cylinder.

Volume of a cylinder = $\pi r^{2}h$

Volume of first cylinder = Volume of new cylinder.

$\pi r_1^2{h}_1=\pi r_2^2{h}_2$

$(18{)}^2\times 30=(12{)}^2\times h_2$

$h_2=\frac{18\times 18\times 30}{12\times 12}=67.5\text{cm}$