Question

The curved surface area of a right circular cone of radius 11.3 cm is 355 $c{m^2}$. What is the slant height of the cone? $\left( {\pi = \dfrac{{22}}{7}} \right)$.

Answer 1

Hint: In this question the curved surface area and radius of a right circular cone is given to us. In order to find the slant height of the right circular cone simply use the direct formula for the curved surface area of the right circular cone which is $C.S.A = \pi rl{\text{ c}}{{\text{m}}^2}$.

Complete step-by-step answer:

Given data

Radius (r) of a right circular cone is 11.3 cm.

Curved surface area (C.S.A) of a right circular cone is 355 $cm^2$.

Then we have to find out the slant height (l) of the right circular cone.

As we know that the curved surface area of the right circular cone is $\pi rl$ $cm^2$.

Where r = radius of the right circular cone.
l = slant height of the right circular cone.
$\Rightarrow C.S.A = \pi rl{\text{ c}}{{\text{m}}^2}$
So substitute the value in the above equation we have,
$\Rightarrow 355 = \dfrac{{22}}{7}\left( {11.3} \right)l$ $\left[ {\because \pi = \dfrac{{22}}{7}} \right]$
So simplify the above equation we have,
$\Rightarrow l = \dfrac{{355 \times 7}}{{22 \times 11.3}} = 10{\text{ cm}}$
So this is the required slant height of the right circular cone.

Note: Whenever we face such types of problems the key concept is simply to have a good gist of the basic direct formula for curved surface area, total surface area for some basic conic sections like cone, hemisphere etc. This will help you get on the right track to get the answer.