Question

The volume of a right circular cone is $9856c{m}^3$. If the diameter of the base is 28cm, find:
(iii) curved surface area of the cone.
$[Assume\pi =\frac{22}{7}]$

Answer 1

Radius of the cone $=\left(\frac{28}{2}\right)cm=14cm$
Let the height of the cone be h.
Volume of the cone $=9856c{m}^3$
$\Rightarrow \frac{1}{3}\pi r^{2}h=9856c{m}^3\Rightarrow [\frac{1}{3}\times \frac{22}{7}\times (14{)}^2\times h]c{m}^3=9856c{m}^{3}h=48cm$
Therefore,the height of the cone is 48 cm.
Slant height (l) of the cone $=\sqrt{r^2+h^2}$
$=\lfloor \sqrt{(14{)}^2+({48}^2)}\rfloor$
$=\left[\sqrt{196+2304}\right]cm$
$=50cm$
Therefore, the slant height of the cone is 50 cm.

CSA of cone$=\pi rl$
$=(\frac{22}{7}\times 14\times 50)c{m}^2$
$=2200c{m}^2$
Therefore, curved surface area of the cone is $2200c{m}^2$.