Question

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

Answer 1

Given: Radius, $r=7cm$ and, height, $h=24m$

Let slant height be ${}^{\prime }{l}^{\prime }$

We know that

$l^2=h^2+r^2$

$\Rightarrow l^2={24}^2+7^2$

$\Rightarrow l^2=576+49$

$\Rightarrow l^2=625$

$\Rightarrow l=\sqrt{625}=25cm$

Curved surface area of $1$ jokers cap $=\pi rl$

$=\frac{22}{7}\times 7\times 25$

$=22\times 25$

$=550c{m}^2$

So, the area of the sheet required to make $1$ joker cap $=$ Curved Surface area of cone $=550c{m}^2$

The area of the sheet required to make $10$ jokers caps $=10\times 550=5500c{m}^2$