Question

What is the formula for the lateral surface area of the given frustum:

Where,
$R_1$ = radius of the base
$L$ = length of lateral side of the bigger cone of which the frustum is a part
$R_2$ = radius of the top surface
$l$ = length of lateral height of cone - lateral height the frustum (s)

• A. $\pi (R_{1}L-R_{2}l)$
• B. $\pi R_1^{2}h-\pi R_{2}l$
• C. $\pi (R_1^{2}h-R_2^{2}l)$
• D. $Noneofthese$

Answer 1

The correct option is A $\pi (R_{1}L-R_{2}l)$

Lateral surface area of the bigger cone of which the frustum is a part
=$\pi R_{1}L$

Lateral surface area of the cone which is removed from the bigger cone
=$\pi R_2{L}_{cone}$

Now,
$L_{cone}=\text{Slant height of the bigger cone}-\text{Slant height of the frustum}$
$\Rightarrow L_{cone}=L-s$

Lateral surface area of the cone which is removed from the bigger cone
=$\pi R_2(L-s)$
=$\pi R_{2}l$

$\therefore$ Lateral surface area of the frustum
= Lateral surface area of the bigger cone of which the frustum is a part - Lateral surface area of the cone which is removed from the bigger cone
=$\pi R_{1}L-\pi R_{2}l$
The lateral surface area of frustum $=\pi (R_{1}L-R_{2}l)$