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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 $$21\ cm$$.

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