Answer: The correct option is (A) 2120 m³.
Step-by-step explanation: Given that a cone-shaped pile of gravel has a diameter of 30 m and a height of 9.1 m.
We are to select the correct option that estimate best approximates the volume of the pile of gravel.
The VOLUME of a cone with radius 'r' units and height 'h' units is given by the formula:
[tex]V=\dfrac{1}{3}\pi r^2h.[/tex]
In the given cone-shaped pile, diameter of gravel is 30 m, so its radius will be
[tex]r=\dfrac{30}{2}=15~\textup{m},[/tex]
and height, h = 9.1 m.
Therefore, the volume of the cone-shaped pile is
[tex]V\\\\\\=\dfrac{1}{3}\pi r^2h\\\\\\=\dfrac{1}{3}\times 3.14 \times 15^2\times 9.1\\\\\\=3.14\times 75\times 9.1\\\\=2143.05~\textup{m}^3[approx].[/tex]
Out of the given options, only 2120 is the nearest one, so the best approximate will be 2120 m³.
Thus, (A) is the correct option.
