a sand pile in a shape of an upside-down cone has a volume of 350 m2 . The diameter of the base pof the pile is 7m. what is the height of the sand pile?

recall that V = 1/3 Bh = 1/3 pi r^2 h

350 = 1/3 (pi * (7/2)^2)h
h = 600/(7pi)

To find the height of the sand pile, we can use the formula for the volume of a cone.

The formula for the volume of a cone is: V = (1/3) * π * r² * h

Given that the volume of the sand pile is 350 m³ and the diameter of the base is 7m, we can find the radius (r) and then use the formula to solve for the height (h).

First, let's find the radius (r):
The diameter is given as 7m, so the radius is half of the diameter.
r = 7m / 2 = 3.5m

Now, we can plug the values into the formula and solve for the height (h):

350 m³ = (1/3) * π * (3.5m)² * h

To isolate h, we can divide both sides of the equation by [(1/3) * π * (3.5m)²]:
h = 350 m³ / [(1/3) * π * (3.5m)²]

Simplifying further:
h = 350 m³ / [(1/3) * π * 12.25m²]
h = 350 m³ / [(1/3) * 3.14 * 12.25m²]
h = 350 m³ / (0.33 * 12.25m²)
h = 350 m³ / 4.03725m²
h ≈ 86.64 m

Therefore, the height of the sand pile is approximately 86.64 meters.