Question

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

height of the cone.

• A. $48cm$
• B. $78cm$
• C. $46cm$
• D. $28cm$

Answer 1

The correct option is A): $48cm$

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 $\left(r\right)=\frac{d}{2}=\frac{28cm}{2}=14cm$.

Hence, volume of this cone $=\frac{1}{3}\pi r^{2}h$

$\Rightarrow \frac{1}{3}\times \frac{22}{7}\times {\left(14\right)}^2\times h=9856{cm}^3$

$\Rightarrow \frac{1}{3}\times \frac{22}{7}\times 14\times 14\times h=9856c{m}^3$

$\Rightarrow h=\frac{1}{14}\times \frac{1}{14}\times \frac{3}{1}\times \frac{7}{22}\times 9856c{m}^3$

$\Rightarrow h=3\times 16cm$

$\Rightarrow h=48cm$

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

Hence, Option A is correct.