Question

The volume of a cylinder is $150\pi c{m}^3$ and its height is $6cm.$ Find the area of its total surface and lateral surface.

Answer 1

Given: Volume of cylinder $=150\pi c{m}^3=150\times \frac{22}{7}c{m}^3$

and, height, $h=6cm$

The volume of the cylinder is given by $\pi \times r^2\times h$

$\Rightarrow \frac{22}{7}\times radiu{s}^2\times height=150\times \frac{22}{7}$

$\Rightarrow radiu{s}^2=150\times \frac{22}{7}\times \left(\frac{7}{22}\right)\times \frac{1}{height}$

$\Rightarrow r^2=150\times \frac{1}{6}=25$

$\Rightarrow r^2=5\times 5$

$\Rightarrow r=5$

Total surface area $=2\times \pi \times r(r+h)$

$=2\times \frac{22}{7}\times 5(5+6)$

$=2\times \frac{22}{7}\times 5\times 11=345.7c{m}^2$

lateral surface area $=2\times \pi \times r\times h$

$=2\times \frac{22}{7}\times 6\times 5=188.5c{m}^2$