Question

Find the volume of a right circular cone that has a height of $5.7\mathrm{m}$ and a base with a circumference of $2.3\mathrm{m}$. Round your answer to the nearest tenth of a cubic meter.

Answer 1

Step-1: Finding the radius of the base:

Given: Height $\mathrm{h}=5.7\mathrm{m}$, circumference of base $=2.3\mathrm{m}$

Let radius of the base of right circular cone be $\mathrm{r}$

Then circumference of base $=2\mathrm{\pi r}$

$\Rightarrow$ $2.3=2\mathrm{\pi r}$

$\Rightarrow$ $\frac{1.15}{\mathrm{\pi }}=\mathrm{r}$

Therefore, radius of the base of the cone is $\frac{1.15}{\mathrm{\pi }}\mathrm{m}$.

Step-2: Finding the volume of the cone:

Let $r$ be the radius and $h$ be the height of the a cone.

We know that the volume of a cone $=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

$=\frac{1}{3}\mathrm{\pi }{\left(\frac{1.15}{\mathrm{\pi }}\right)}^2\left(5.7\right)$

$=\frac{{\left(1.15\right)}^2}{\mathrm{\pi }}\times \left(1.9\right)$

$=\frac{1.3225}{3.14}\times \left(1.9\right)\left[\mathrm{\pi }=3.14\right]$

$=0.8002$

$\approx 0.8{\mathrm{m}}^3$ [Rounded to the nearest tenth]

Hence, the volume of a right circular cone is $0.8{\mathrm{m}}^3$.