Question

Find the volume of a right circular cone that has a height of 12.1 m and a base with a circumference of 17.7 m. Round your answer to the nearest tenth of a cubic meter.

Answer 1

The volume of a right circular cone is

$V=\dfrac{1}{3}\pi r^2\cdot h$.

If a circumference of a base circle is 17.7 m, then using formula $l=2\pi r$ for circumference of a circle, you can find the radius:

$17.7=2\pi r,\\ \\ r=\dfrac{17.7}{2\pi} =\dfrac{8.85}{\pi}$.

Then the volume is:

$V=\dfrac{1}{3}\pi r^2\cdot h =\dfrac{1}{3}\pi \left(\dfrac{8.85}{\pi}\right)^2\cdot 12.1=\dfrac{315.90075}{\pi}$.

Answer 2

Answer:

$V_{cone}=100.6 m^{3}$

Step-by-step explanation:

The volume of a cone is defined as:

$V_{cone}=\frac{1}{3}A_{base}h$

So, a cone has a circular base, and its area is:

$A_{base}=\pi r^{2}$

Replacing this relation in the volume equation:

$V_{cone}=\frac{1}{3}\pi r^{2}h$

Now, the problem gives us the height but no the radius, instead it gives the circumference length, which we can use to find the radius:

$L=2\pi r\\r=\frac{L}{2 \pi}\\ r=\frac{17.7m}{2 \pi}\\r=\frac{8.85}{\pi}m$

Then, we use this radius to find the volume:

$V_{cone}=\frac{1}{3}\pi (\frac{8.85}{\pi}m)^{2}12.1m$

$V_{cone}=\frac{315.9}{\pi} m^{3}$

Using $\pi \approx 3.14$:

$V_{cone}=\frac{315.9}{3.14} m^{3}=100.6 m^{3}$

Therefore, the volume is $V_{cone}=100.6 m^{3}$