Question

The volume of a right circular cone is $9856{cm}^3$. If the diameter of the base if $28cm$, find curved surface area of the cone in $c{m}^2$.

• A. $210$
• B. $454$
• C. $874$
• D. None of the above

Answer 1

The correct option is D None of the above

Given, volume of the right circular cone $=9856c{m}^3$ and diameter of the base $=28cm$.
Then, radius of the base $=14cm$.

According to the given condition,
Volume of cone $V=\frac{1}{3}\pi r^{2}h=9856$

$⟹\frac{1}{3}\times \frac{22}{7}\times {14}^2\times h=9856⟹h=48cm$.

We know that, $l^2=r^2+h^2$
$⟹l^2={14}^2+{48}^2=196+2304=2500⟹l=50cm$.

Now, CSA of cone $=\pi rl=\frac{22}{7}\times 14\times 50=2200c{m}^2$.

Hence, option $D$ is correct.