Question

How many cubic meters of dirt are there in a pile, conical in shape, 9 m in diameter & 4 m high?

Answer 1

To solve this question we will use the following formula for the volume of a cone:

$\begin{gathered} V=\frac{1}{3}\pi r^2h, \\ \text{where r is the radius of the cone and h is its height.} \end{gathered}$

Substituting

$\begin{gathered} r=\frac{9m}{2}=4.5m, \\ h=4m, \end{gathered}$

we get:

$\begin{gathered} V=\frac{1}{3}\pi(4.5m)^2\cdot4m \\ =\frac{1}{3}\pi(20.25m^3)\cdot4m \\ =27\pi m^3 \\ \approx84.8m^3. \end{gathered}$

Answer:

$84.8m^3.$