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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