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Question

The 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 are of the cone.

Solution
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Consider $$r$$ as the radius of the cone

It is given that

Slant height of the cone $$=14\ cm$$

Curved surface area of the cone $$=308\ cm^{2}$$

It can be written as

$$\pi rl=308$$

By substituting the values

$$\dfrac{22}{7}\times r\times 14=308$$

On further calculation

$$22\times r\times 2=308$$

So we get

$$r=\dfrac{308}22\times 2)$$

$$r=7\ cm$$

We know that

Total surface area of a cone $$=\pi rl(1+r)$$

By substituting the values

Total surface area of cone $$=\dfrac{22}{7}\times 7\times (14+7)$$

On further calculation

Total surface area of a cone $$=22\times 21=462\ cm^{2}$$

Therefore, the base radius of the cone is $$7\ cm$$ and the total surface area is $$462\ cm^{2}$$

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