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Curved surface area of a cone is $308\ cm^2$ and its slant height is $14\ cm$. Find the radius of the base and total surface area of the cone.
Given:
The curved surface area of a cone is $308\ cm^2$ and its slant height is $14\ cm$.
To do:
We have to find the radius of the base and the total surface area of the cone.
Solution:
The curved surface area of the cone $= 308\ cm^2$
Slant height of the cone $(l) = 14\ cm$
This implies,
Radius of the base of the cone $(r)=\frac{\text { Curved surface }}{2 \pi h}$
$=\frac{308 \times 7}{22 \times 14}$
$=7 \mathrm{~cm}$
The total surface area of the cone $=\pi r l+\pi r^{2}$
$=308+\frac{22}{7} \times 7 \times 7$
$=308+154$
$=462 \mathrm{~cm}^{2}$
Hence, the radius of the base and the total surface area of the cone are $7 \mathrm{~cm}$ and $462 \mathrm{~cm}^{2}$ respectively.
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