Question

The height and the radius of a cylinder are $7.5cm$ and $3.5cm$ respectively. Find the ratio of its total surface area and curved surface area.

Answer 1

Given,Height of cylinder $\left(h\right)=7.5cm$ Radius $\left(r\right)=3.5cm$
Total surface area $=2\pi r(h+r)$
$\begin{array}{c}=2\times \frac{22}{7}\times 3.5\times (7.5+3.5)\\ =22\times 11\\ =242{cm}^2\end{array}$
Curved surface area
$\begin{array}{cc}& =2\pi rh\\ & =2\times \frac{22}{7}\times 3.5\times 7.5\\ & =22\times 7.5\\ & =165{cm}^2\end{array}$
$\therefore \frac{\text{Total surface area of cylinder}}{\text{Curved surface area}}=\frac{2\pi r(h+r)}{2\pi rh}$
$\begin{array}{cc}& =\frac{h+r}{h}\\ & =\frac{7.5+3.5}{7.5}\\ & =\frac{11\times 10}{75}=\frac{22}{15}\end{array}$
Hence, required ratio $=22:15$