Question

Find the total surface area of a cone whose slant height is 9m and radius of the base is 14m.

Answer 1

Hint: The formula for the total surface area can be found out as $ A = \pi r\left( {r + l} \right) $ , where $ r $ is the radius of the base of the cone, $ l $ is slant height of the cone.

Complete step-by-step answer:
The slant height of the given cone is 9 m. Also, the radius of the base of the cone is given as 14 m.
As shown in the diagram, $ h $ is the slant height of the cone and $ r $ is the radius of the base of the cone.

We know that the total surface area of the cone is given by $ A = \pi r\left( {r + l} \right) $
Now, we can substitute 9 for $ h $ and 14 for $ r $ , in the formula to find the total surface area of the cone.
Total surface area of the cone,
 $
\Rightarrow A = \pi r\left( {r + l} \right)\\
 = \pi \cdot 14\left( {14 + 9} \right)\\
 = 14\pi \left( {23} \right)\\
 = \dfrac{{22}}{7} \cdot 14 \cdot 23
 $

Therefore, the total surface area of the cone is $ 1012{\rm{ }}{{\rm{m}}^2} $.

Additional Information:
A three-dimensional solid that tapers smoothly from a smooth circular base is called a cone.
The base shape of the cone is a circle. Cone has a single face and has a base similar to the cylinder.
The volume of a cone can be given by $ V = \dfrac{1}{3}\pi {r^2}h $ , where $ r $ is the radius of the base of the cone and $ h $ is the slant height of the cone. The total surface area of the cone is given by $ A = \pi r\left( {r + l} \right) $ .

Note: Remembering formulae becomes tedious sometimes and students often make mistakes while writing the formula for total surface area of the cone. If they understand how the formula has arrived, it would be easier for them to remember it.
There is a chance of calculation mistakes in this type of question, so handle the calculation part with care.