Question

A cone with height 8 ft and radius 4 ft, pointing downward, is filled with water to a depth of 2 ft. All of the water will be pumped out over the top of the cone. The density of water is 62.4 lb/ ft3. (a) Consider a slice of water that is Δh ft thick and located h ft from the bottom of the cone. Use Delta or the CalcPad for Δ. Leave π in your answer. Volume of slice = ft3 Displacement of slice = ft (b) Find the endpoints of the integral needed to find the exact work required to pump all the water out over the top. Lower endpoint = Upper endpoint =

Answer 1

To find the endpoints of the integral needed to find the exact work required to pump all the water out over the top, we can divide the cone into small slices, each with a thickness of Δh and located at a height of h from the bottom of the cone. The volume of each slice is given by the formula V = (1/3)πr²Δh, where r is the radius of the cone. The displacement of each slice is given by the formula d = h + (8 - h - 2) = 10 - h. Therefore, the endpoints of the integral are h = 0 and h = 8 ft.

Step-by-step explanation:

To find the endpoints of the integral needed to find the exact work required to pump all the water out over the top, we need to consider the height of the water in the cone and how it changes as we move up the cone. We can divide the cone into small slices, each with a thickness of Δh and located at a height of h from the bottom of the cone.

The volume of each slice is given by the formula V = (1/3)πr²Δh, where r is the radius of the cone.

The displacement of each slice is given by the formula d = h + (8 - h - 2) = 10 - h. Therefore, the endpoints of the integral are h = 0 and h = 8 ft.