Question

A solid cylindrical pipe made of wax has a radius of 2 cm and height equal to 14 cm. It is melted and recast into a solid prism of base area $16c{m}^2.$ What will be the height of the prism?

Answer 1

Given:
Radius of the cylinder = 2 cm
Height of the cylinder = 14 cm

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

$=\pi \times (2{)}^2\times 14$

$=\frac{22}{7}\times 2\times 2\times 14$

$=176c{m}^3$

Now, it is recast into a solid prism.

$\therefore$ Volume of the cylinder = Volume of the solid prism

$\Rightarrow 176=\text{Base Area}\times h$

$\Rightarrow 176=16\times h$
$\Rightarrow h=\frac{176}{16}=11cm$

Hence, height of the prism = 11 cm