Question

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

Answer 1

Let $l$ be the slant height of the cap.

Given:-

Radius of cap $\left(r\right)=7cm$

Height of cap $\left(h\right)=24cm$

Therefore,

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

$\Rightarrow l^2={\left(24\right)}^2+{\left(7\right)}^2$

$\Rightarrow l^2=576+49$

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

Now,

Curved surface area of cap $=$ Curved surface area of cone

As we know that,

Curved surface area of cone $=\pi rl$

Therefore,

Curved surface area of cap $=\frac{22}{7}\times 7\times 25=550{cm}^2$

Now,

C.S.A. of $1$ cap $=550{cm}^2$

C.S.A. of $10$ caps $=550\times 10=5500{cm}^2$

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

Hence the correct answer is $5500{cm}^2$.