Question

The volume of a right circular cone is $9856c{m}^3$. If the diameter of the base is $28cm$, find
(i) Height of the cone.
(ii) Slant height of the cone.
(iii) curved surface area of the cone.

Answer 1

Given:

$r=\frac{28}{2}=14$cm

$\left(i\right)$Let height $=h$

$\Rightarrow$Volume $=9856=\frac{1}{3}\pi r^{2}h$

$9856=\frac{1}{3}\times \frac{22}{7}\times 14\times 14\times h$

$\Rightarrow$$h=48$cm

$\left(ii\right)\Rightarrow$Slant height $=\sqrt{r^2+h^2}=\sqrt{{14}^2+{48}^2}=\sqrt{196+2340}=50$cm

$\left(iii\right)\Rightarrow$Curved Surface Area $=\pi rl=\frac{22}{7}\times 14\times 50$cm${}^2$

$=22004$cm${}^2$