Recall that work is defined to be force times distance, and that the weight (force) of a liquid is equal to its volume times its density. A fish tank has a rectangular base of width 2 feet and length 6 feet and sides of height 5 feet. If the tank is filled with water weighing 62.5 lb per cubic foot, the work required to pump all the water just over the top of the tank is:

A.) 781.24 ft-lb
B.) 150.0 ft-lb
C.) 9375.o ft-lb
D.) 3750.0 ft-lb
E.) 865.0 ft-lb

9,375

W = 62.5 * 12 integral of (5-y) dy from 0 to 5

Area of each water slice = 12
You have to pump each slice out. An illustration would make you understand better, but I have no way to show you. So, the answer is 9375 lb-ft.

Well, let me break it down for you. Now, the first step is to calculate the volume of the fish tank, which is simply the length times the width times the height.

So, the volume of the fish tank would be:
Volume = length × width × height
Volume = 6 ft × 2 ft × 5 ft
Volume = 60 cubic feet

Now, we know that the weight of the water is 62.5 lb per cubic foot. So, we can find the weight of the water in the tank by multiplying the volume by the weight per cubic foot.

Weight = volume × weight per cubic foot
Weight = 60 cubic feet × 62.5 lb/cubic foot
Weight = 3750 lb

Almost there! Now, to find the work required to pump all the water just over the top of the tank, we use the formula work = force × distance. In this case, the force is the weight of the water and the distance is the height of the tank.

Work = force × distance
Work = 3750 lb × 5 ft
Work = 18,750 ft-lb

So, the correct answer would be D) 3750.0 ft-lb.

Now, wasn't that "fin"-tastic? I always get a little "tankful" when it comes to answering questions!

To find the work required to pump all the water just over the top of the tank, we need to calculate the weight of the water and then multiply it by the height of the tank.

First, we need to find the volume of the tank. The volume of a rectangular tank is given by the formula: volume = length * width * height.
In this case, the length is 6 feet, the width is 2 feet, and the height is 5 feet.

Volume of the tank = 6 feet * 2 feet * 5 feet = 60 cubic feet.

Next, we can calculate the weight of the water in the tank. The weight of a liquid is equal to its volume multiplied by its density.
In this case, the density of water is given as 62.5 lb per cubic foot, and the volume of water in the tank is 60 cubic feet.

Weight of the water = 60 cubic feet * 62.5 lb per cubic foot = 3750 lb.

Finally, we can calculate the work required to pump all the water just over the top of the tank by multiplying the weight of the water by the height of the tank, which is 5 feet.

Work required = 3750 lb * 5 feet = 18750 ft-lb.

Therefore, the correct answer is C.) 9375.0 ft-lb.

To find the work required to pump all the water just over the top of the tank, we need to determine the total weight of the water and then multiply it by the distance over which it is lifted.

First, let's find the volume of the tank. The tank has a rectangular base with a width of 2 feet and a length of 6 feet, and the sides have a height of 5 feet. The volume of a rectangular prism is given by the formula: volume = length x width x height.

So, the volume of the tank is: volume = 6 ft x 2 ft x 5 ft = 60 cubic feet.

Next, we need to find the weight of the water. We are given that the density of the water is 62.5 lb per cubic foot. The weight is equal to the volume times the density: weight = volume x density.

So, the weight of the water in the tank is: weight = 60 ft^3 x 62.5 lb/ft^3 = 3750 lb.

Finally, we can find the work required to lift the water just over the top of the tank. The work is equal to the weight times the distance: work = weight x distance.

However, the question does not provide the distance over which the water is lifted. Therefore, we cannot find the exact value of the work required without additional information.