Curved surface area of a cone is $308 \mathrm{~cm}^{2}$ and its slant height is $14 \mathrm{~cm}$.
Question. Curved surface area of a cone is $308 \mathrm{~cm}^{2}$ and its slant height is $14 \mathrm{~cm}$. Find

(i) radius of the base and

(ii) total surface area of the cone.

$\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$


Solution:

(i) Slant height (l) of cone $=14 \mathrm{~cm}$

Let the radius of the circular end of the cone be $r$.

We know, CSA of cone $=\pi r$

$(308) \mathrm{cm}^{2}=\left(\frac{22}{7} \times r \times 14\right) \mathrm{cm}$

$\Rightarrow r=\left(\frac{308}{44}\right) \mathrm{cm}=7 \mathrm{~cm}$

Therefore, the radius of the circular end of the cone is 7 cm.

(ii) Total surface area of cone $=$ CSA of cone $+$ Area of base

$=\pi r l+\pi r^{2}$

$=\left[308+\frac{22}{7} \times(7)^{2}\right] \mathrm{cm}^{2}$

$=(308+154) \mathrm{cm}^{2}$

$=462 \mathrm{~cm}^{2}$

Therefore, the total surface area of the cone is $462 \mathrm{~cm}^{2}$.
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