Question

The height of a cone is $21cm$. Find the area of the base if the slant height is $28cm$.

Answer 1

Step 1: Find the radius of the cone.

Let the radius of the cone be $rcm$

Given that, the height $h$ of the cone is $21cm$ and the slant height of the cone is $28cm$

According to the Pythagoras theorem, $l^2=h^2+r^2$

$$\begin{gathered} \Rightarrow {\left(28\right)}^2={\left(21\right)}^2+r^2 \\ \Rightarrow 784=441+r^2 \\ \Rightarrow r^2=784-441 \\ \Rightarrow r^2=343 \\ \Rightarrow r=7\sqrt{7}cm \end{gathered}$$

Step 2: Find the area of the base of cone

Area of base of the cone of radius $r$ $=\pi r^2$

$$\begin{gathered} =\frac{22}{7}\times {\left(7\sqrt{7}\right)}^2 \\ =\frac{22}{7}\times 7\sqrt{7}\times 7\sqrt{7}\left(\pi =\frac{22}{7}\right) \\ =22\times 49 \\ =1078c{m}^2 \end{gathered}$$

Therefore, the area of the base is $1078c{m}^2$