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A joker's cap is in the form of a right circular cone of base radius $ 7 \mathrm{~cm} $ and height $ 24 \mathrm{~cm} $. Find the area of the sheet required to make 10 such caps.
Given:
A joker’s cap is in the form of a right circular cone of base radius $7\ cm$ and height $24\ cm$.
To do:
We have to find the area of the sheet required to make 10 such caps.
Solution:
The radius of the base of the conical cap $(r) = 7\ cm$
Height of the cap $(h) = 24\ cm$
Therefore,
Slant height of the cap $=\sqrt{r^{2}+h^{2}}$
$=\sqrt{(7)^{2}+(24)^{2}}$
$=\sqrt{49+576}$
$=\sqrt{625}$
$=25 \mathrm{~cm}$
Area of the slant surface $=\pi r l$
$=\frac{22}{7} \times 7 \times 25$
$=550 \mathrm{~cm}^{2}$
Area of 10 such caps $=550 \times 10$
$=5500 \mathrm{~cm}^{2}$
Therefore, the area of the sheet required to make 10 such caps is $5500 \mathrm{~cm}^{2}$.
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