Question

A clown's cap is in the form of a right circular cone of base radius $7$cm and height $24$cm. Find the area of the sheet required to make $10$ such caps.

Answer 1

It is given that the height of the conical cap is $h=24$ cm andthe radius is $r=7$ cm, therefore, the slant height of the conical cap is:

$l^2=h^2+r^2={24}^2+7^2=576+49=625\Rightarrow l^2=625\Rightarrow l=\sqrt{625}=25$

Thus, slant height of the cone is $25$ cm.

We also know that the curved surface area of a cone with radius $r$ and slant height $l$ is $CSA=\pi rl$.

Here, the slant height of the cone is $l=25$ cm and radius is $7$ cm, therefore,

$CSA=\pi rl=\frac{22}{7}\times 7\times 25=22\times 25=550$cm${}^2$

Now, for $1$ cap, the sheet required is $550$cm${}^2$ and the area of sheet required for $10$ caps is:

$550\times 10=5500$cm${}^2$

Hence, the area of sheet required to make $10$ caps is $5500$ cm${}^2$.