Question

The volume of a cone is 8π ft^3. What is the radius of the cone?

If you can help with this ASAP that would be great!

Answer 1

first off, let's notice something, hmm the volume is in ft³, however the height is 6 meters, so hmmm and we need the radius is meters as well, so we'd need to convert the ft³ to m³, keeping in mind 1m³ has 35 ft³.

`\begin{array}{ccll} m^3&ft^3\\ \cline{1-2} 1 & 35\\ x& 8\pi \end{array} \implies \cfrac{1}{x}~~=~~\cfrac{35}{8\pi }\implies \cfrac{8\pi }{35}=x`

now, let's check its volume then

`\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=(8\pi)/(35) ~m^3\\ h=6~m \end{cases}\implies \cfrac{8\pi }{35}=\cfrac{\pi r^2(6)}{3}\implies \cfrac{8\pi }{35}=2\pi r^2 \\\\\\ \cfrac{8\pi }{35\cdot 2\pi }=r^2\implies \cfrac{4}{35}=r^2\implies \sqrt{\cfrac{4}{35}}=r\implies \stackrel{ meter }{0.72}\approx r`