Answer:
[tex]V=\frac{1}{3}\pi h^3[/tex]
Step-by-step explanation:
It is given that the shape of a pile of sand is conical.
Diameter of cone is twice the height.
Let height of cone be h.
Diameter of cone = 2h
Radius of the cone = [tex]\frac{2h}{2}=h[/tex]
It means radius of the cone is h.
Volume of cone is
[tex]V=\frac{1}{3}\pi r^2h[/tex]
where, r is radius and h is height of the cone.
Substitute r=h in the above formula.
[tex]V=\frac{1}{3}\pi (h)^2h[/tex]
[tex]V=\frac{1}{3}\pi (h)^{2+1}[/tex]
[tex]V=\frac{1}{3}\pi (h)^{3}[/tex]
Therefore, the volume of pile of sand is [tex]V=\frac{1}{3}\pi h^3[/tex].
