A tank in the shape of a right circular cylinder is filled with water (62.5 lb/ft3). It has a height of 8 ft and a diameter of 10 ft. How much work is required to pump all the water to a spout that is 3 ft above the top of the tank?
To find the work required to pump all the water, we need to calculate the weight of the water and then determine the work done against gravity to lift it to the spout.
First, let's find the volume of the tank. Since the tank is a right circular cylinder, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
Given:
Height of the tank (h) = 8 ft
Diameter of the tank = 10 ft
We need to find the radius (r) using the formula for diameter: d = 2r.
Given:
Diameter (d) = 10 ft
Using the formula, we can solve for r:
10 ft = 2r
r = 10 ft / 2 = 5 ft
Now we can find the volume of the tank using the radius and height:
V = π(5 ft)^2(8 ft)
V = π(25 ft^2)(8 ft)
V = π(200 ft^3)
To find the weight of the water, we need to multiply the volume by the density of water. Given:
Density of water = 62.5 lb/ft^3
Weight of water = Density × Volume
Weight of water = (62.5 lb/ft^3) × (π(200 ft^3))
Now let's calculate the work done against gravity to lift the water to the spout.
The work done against gravity is given by the formula: work = force × distance
The force required to lift the water is equal to its weight, and the distance is the height of the spout above the top of the tank, which is given as 3 ft.
So, the work required will be: work = weight of water × distance
work = (Weight of water) × (3 ft)
Finally, calculate the work required to pump all the water to the spout.