Question

Diameter of the base of a cone is 10.5cm and its slant height is 10cm. Find its curved surface area.

Answer 1

Hint: In this question, we are given the diameter of the base of a cone and its slant height and we have to find its curved surface area. For this, we will use a formula of curved surface area of cone which is given as $\text{Area of cone}=\pi rl$ where r is radius of base of cone and l is the slant height. Here, we are given diameter, so first we will find the radius by dividing diameter by 2.

Complete step by step answer:
Let us first draw a diagram to understand measurements easily.

Here we are given the diameter of the base of the cone and slant height of the cone. We have to find the curved surface area of the cone. Curved surface area of the cone is the area of the curved part of the cone excluding its area of base. Formula for finding curved surface area of cone is given by $\text{CSA}=\pi rl$ where CSA represents curved surface area, r represents radius of base of cone and l is the slant height.
As we are given diameter of base of cone, so let’s find radius of base of cone using diameter.
Radius of base of cone $\Rightarrow \dfrac{\text{Diameter}}{2}=\dfrac{10.5}{2}=5.25cm$.
So, r = 5.25cm.
Slant height of cone is given as 10cm.
So, l = 10cm.
Curved surface area of cone $\Rightarrow \pi rl=\pi \times 5.25\times 10$.
As we know, $\pi =\dfrac{22}{7}$ and 5.25 can be written as $\dfrac{525}{100}$. So we get:
$\begin{align}
  & \Rightarrow \dfrac{22}{7}\times \dfrac{525}{100}\times 10 \\
 & \Rightarrow 165c{{m}^{2}} \\
\end{align}$

Hence, the curved surface area of the cone is $165c{{m}^{2}}$.

Note: Students should not get confused between slant height and height of the cone. For formula of curved surface area, slant height is used but if we are given height of cone, than slant height can be found by using the formula $l=\sqrt{{{h}^{2}}+{{r}^{2}}}$ where l is slant height, h is height and r is radius of base of cone. Student should note that, it is necessary to write units of every measurement. After calculating the area, we use the squared units. Take care while solving calculations involving decimal points.