Question

A solid cylinder has a total surface area of $462c{m}^2$, if its curved surface area is one third of its total surface area. find the radius and height of the cylinder

Answer 1

Total surface area of the cylinder $\left(TSA\right)=462c{m}^2$

curved surface of the cylinder $\left(CSA\right)=\frac{1}{3}$ of TSA

$=\frac{1}{3}\times 462$

$=154c{m}^2$

Area of each circle $=\frac{TSA-CSA}{2}=\frac{(462-154)}{2}$ [$\because$ TSA = CSA + 2 circular base area]

$=154c{m}^2$

$\therefore \pi \times r^2=154$ [$\because$ Area of the circle $=\pi r^2$]

$\Rightarrow r^2=49$

$\Rightarrow r=7$

And, $2\pi rh=154$ [$\because$ curved surface of the cylinder $=2\pi rh$ ]

$2\times \frac{22}{7}\times 7\times h=154$

$\Rightarrow h=\frac{154}{44}$

$\Rightarrow h=3.5$