Question

The radii of the circular ends of a frustum of height $6cm$ are $14cm$ and $6cm$ respectively. Find the lateral surface area and total surface area of the frustum.

Answer 1

We have
$r_1=14cm;r_2=6cm;h=6cm$

Let $l$ be the slant height of the frustum.

Then $l=\sqrt{h^2+{\left(r_1{-r}_2\right)}^2}cm\Rightarrow l=\sqrt{36+64}cm=10cm$

Lateral surface area$=\pi \left(r_1{+r}_2\right)l$$=\frac{22}{7}\times (14+6)\times 10{cm}^2=628.57{cm}^2$

total surface area $=\pi \{r_1^2+r_2^2+(r_1+r_2\left)l\right\}$

$=\frac{22}{7}\times (196+36+20\times 10){cm}^2=1357.71{cm}^2$