Question

Find the total surface area of the cone, if its slant height is 21 m and diameter of its base is 24 m. $\left( \text{Assume }\pi =\dfrac{22}{7} \right)$

Answer 1

Hint: Substitute the dimensions provided in the formula of the total surface area of the cone.

Complete step-by-step answer:
The surface area of a solid object is a measure of the total area that the surface of the object occupies. The total surface area of the cone is the sum of areas of the base circle and the top slant surface. So, to define the total surface area the radius of the base circle and slant height of the cone must be known.
The total surface area can be expressed as: $\pi {{r}^{2}}+\pi rl\ldots (1)$.
According to our question, we are given that the slant height of the cone is 21 m and diameter of the base is 24 m. So, the radius of the base circle is 12 m.

Now, putting this data in equation 1 we get,
$\begin{align}
  & \pi \cdot {{(12)}^{2}}+\pi \cdot (12)\cdot (21) \\
 & 144\pi +252\pi =396\pi \\
 & \Rightarrow 396\times \dfrac{22}{7}=1244.571{{m}^{2}} \\
\end{align}$
So, the total surface area of the cone is 1244.571 m².

Note: The key step for solving this problem is the knowledge of the total surface area of the cone which is the sum of areas of base circle and top slant surface. By using this definition, we formulate the total surface area of the cone. After putting values in the formula, the total surface area of the cone is evaluated correctly.