Question

# Total surface area of a cone is $$616\ sq.cm$$ If the slant height of the cone three times the radius of its base, find its slant height.

Solution

## Let the radius of base and slant height of the cone $$r$$ cm and $$I$$ cm, respectively.Slant height of the cone $$=3\times$$Radius of the cone    (given)$$\therefore I=3r$$Total surface area of the cone $$=616\ cm^2$$$$\therefore \pi r(r+I)=616\ cm^2$$$$\Rightarrow \dfrac{22}{7}\times r\times (r+3r)=616$$$$\Rightarrow \dfrac{22}{7}\times r\times 4r=616$$$$\Rightarrow \dfrac{88}{7}r^2=616$$$$\Rightarrow r^2=\dfrac{616\times 7}{88}=49$$$$\Rightarrow r=\sqrt{49}=7\ cm$$$$\therefore$$ Slant height of the cone, $$I=3r=3\times 7=21\ cm$$Thus, the slant height of the cone is $$21\ cm$$.Maths

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