Question

The volume of a right circular cone is $9856{cm}^3$. If the diameter of the base if $28cm$, find slant height of the cone.

• A. $50cm$
• B. $30cm$
• C. $25cm$
• D. $20cm$

Answer 1

Answer: (A)

$50cm$

We know, Volume of a cone $=\frac{1}{3}\pi r^{2}h$.

Given, diameter of the base $d=28cm$.

Then, Radius of the base $=\frac{d}{2}=\frac{28}{2}=14cm$.

Hence, volume of this cone $=\frac{1}{3}\times \frac{22}{7}\times {14}^2\times h=9856{cm}^3$

Therefore, $h=48cm$.

Hence, height of the cone is $48cm$.

For a cone, slant height $l=\sqrt{h^2+r^2}$

Hence, $l=\sqrt{{48}^2+{14}^2}=\sqrt{2500}$

$⟹$ $l=50cm$.

Therefore, option $A$ is correct.