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 $\left.\pi=\frac{22}{7}\right]$
(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 $462 \mathrm{~cm}^{2}$.
(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 $462 \mathrm{~cm}^{2}$.