Question

Find the volume of a cone with a height of 8 m and a base diameter of 12 mUse the value 3.14 for it, and do not do any rounding.Be sure to include the correct unit in your answer.

Answer 1

The volume V of a cone with radius r and height h is:

`V=(1)/(3)\pi r^(2)h`

And the radius is half the diameter. Since this cone has a diameter of 12 m, the radius is:

`r=(12m)/(2)=6m`

And the height is 8m. Thus, the volume V is:

`\begin{gathered} V=(1)/(3)\pi(6m)^28m \\ \\ V=(\pi)/(3)(36m^2)8m \\ \\ V=(\pi)/(3)(288)(m^2\cdot m) \\ \\ V=\pi\cdot(288)/(3)m^3 \\ \\ V=96\pi m^(3) \end{gathered}`

Now, using 3.14 for π, we obtain:

`\begin{gathered} V=96\cdot3.14m^3 \\ \\ V=301.44m^(3) \end{gathered}`

Therefore, the volume of that cone is 301.44m³.