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Question

Curved surface area of a cone. is $$308\ cm^{2}$$ its slant height is $$14\ cm$$. Find
(i) radius of the base and
(ii) total surface area of the cone.


Solution

Given : 
Curved surface area of the cone $$= 308 cm^2$$ and Slant height or $$l = 14$$ cm.
Curved surface area of the cone $$= πrl$$

$$308 =  \dfrac{22}{7} \times r\times14$$

$$r= \dfrac{(308\times7)}{(22\times14)}$$

$$r = 7 cm$$

Total surface area of the cone $$= πr(r+l)$$

$$= (\dfrac{22}{7}\times7)(7+14)$$

$$= 22\times21$$

Total surface area of the cone $$= 462 cm^2$$

So, the radius of the base of the cone is $$7$$ cm and the total surface area of the cone is $$462 cm^2$$.

Mathematics

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