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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

The volume of this cone is 91,185.6 cubic yards. What is the height of this cone? Use-example-1
User Kuti
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1 Answer

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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

User Donato Azevedo
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