Question

The volume of this cone is 91,185.6 cubic yards. What is the height of this cone? Use pi=3.14 and round your answer to the nearest hundredth

Answer 1

The volume of a cone is given by the formula:

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

Where r is the radius of the base of the cone and h is its height.

From this equation, we can solve for h like this:

`\begin{gathered} V=(1)/(3)\pi hr^2 \\ (V)/(\pi r^2)*3=(1)/(3)(\pi hr^2)/(\pi r^2)*3 \\ (3V)/(\pi r^2)=(3)/(3)(\pi r^2)/(\pi r^2)h \\ h=(3V)/(\pi r^2) \end{gathered}`

Now let's replace the values that we know into this formula

V=91185.6 yd^3

r=44 yd

`\begin{gathered} h=(3V)/(\pi r^2) \\ h=(3*91185.6)/(3.14*44^2)=45 \end{gathered}`

Then, the height of the cone equals 45 yards