Question

Find the total surface area of a cone, If its slant height is 9m and the radius of its base is 12 m.
A. $792{m^2}$
B. $452{m^2}$
C. $682{m^2}$
D. $987{m^2}$

Answer 1

Hint: In order to solve this question, we will use the formula for the total surface area of cone which is given by \[Total\;Surface\;Area = \pi rl + \pi {r^2} = \pi r(r + l)\].
So in this question, slant height and radius of the cone is given. So we just need to put the value of these two variables in the formula and we will get the required answer.

Complete step-by-step answer:

Here,
 r is the radius of the base
 l is the slant height
h is the perpendicular height
Given that l= 9m and r= 12m
The total surface area of cone is given by
\[ = \pi r(r + l)\]
Substituting the values of r and l from the question, we get
 \[ = 722 \times 12 \times \left( {12 + 9} \right) = 792{m^2}\]
Hence, the correct option is “A”

Note: In order to solve such problems students must remember the formula of the total surface area of the cone. Total surface area of the cone comprises the slant area or the area of the outer wall and the area of the circular base. So we find the sum of both.