Question

The total surface area of the cone whose radius is 2r and slant height is $\dfrac{l}{2}$.
A) $2\pi r\left( l+r \right)$
B) $2\pi r\left( \dfrac{l}{2}+r \right)$
C) $2\pi r\left( l+4r \right)$
D) $\pi r\left( l+4r \right)$

Answer 1

Hint: To specify a figure most fundamental quantities are perimeter, area and volume. Area can be defined as the space occupied by a flat shape or the surface of an object. We have an established formula for areas of three-dimensional figures. So, by using this formula we can easily solve our problem.

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 of the cone is the sum of area of the base circle and top surface.
Therefore, 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 $\dfrac{l}{2}$ and radius is 2r.
Now, putting this data in equation (1) we get,
$\begin{align}
  & \Rightarrow \pi \cdot {{(2r)}^{2}}+\pi \cdot (2r)\cdot \left( \dfrac{l}{2} \right) \\
 & \Rightarrow 4\pi {{r}^{2}}+\pi rl \\
 & \Rightarrow \pi r\left( l+4r \right) \\
\end{align}$
Therefore, option (D) is correct.

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. After putting values in the formula, the total surface area of the cone is evaluated correctly.