Grain poured at a certain speed from a chute forms a conical pile that is as high as the diameter of the conical pile. Find the volume and total surface area of such a conical pile of grain that is 3.2 meters in high
Let's denote the radius of the base of the conical pile as r and the height of the conical pile as h. We are given that the height of the conical pile is h = 3.2 meters and the height is equal to the diameter of the base, so the radius of the base is r = h/2 = 3.2/2 = 1.6 meters.
The volume of a cone can be calculated using the formula:
V = (1/3)πr^2h
Substitute the values of r and h into the formula:
V = (1/3)π(1.6)^2(3.2) = 8.53 cubic meters
So, the volume of the conical pile is 8.53 cubic meters.
The total surface area of a cone can be calculated using the formula:
A = πr(r + √(r^2 + h^2))
Substitute the values of r and h into the formula:
A = π(1.6)(1.6 + √(1.6^2 + 3.2^2)) = 17.05 square meters
So, the total surface area of the conical pile is 17.05 square meters.