The inside of a trough is shaped like a rectangular solid, 25 feet long, 6 inches wide, and filled with water to a depth of 35 inches. If we wish to raise the depth of the water to 38 inches, how much water must be let into the tank?

a. 25/96 cubic foot
b. 25/8 cubic feet
c. 75/2 cubic foot
d. 225 cubic feet
e. 450 cubic feet

1/4 ft * 1/2 ft * 25 ft = ? ft^3

sorry how did you get to the answer 25/8?

he just multiplied length,width and depth of water added

To find the amount of water that needs to be let into the trough, we need to calculate the difference in volume between the existing water level and the desired water level.

The volume of a rectangular solid is calculated by multiplying its length, width, and height. In this case, the trough has a length of 25 feet, a width of 6 inches (which we will convert to feet), and a height (the current water depth) of 35 inches (which we will also convert to feet).

Converting inches to feet:
6 inches * (1 foot / 12 inches) = 0.5 feet

35 inches * (1 foot / 12 inches) = 2.9167 feet

Now we can calculate the current volume of water in the trough:
Volume = Length * Width * Height
Volume = 25 feet * 0.5 feet * 2.9167 feet = 36.4583 cubic feet

Next, we need to calculate the volume of water needed to raise the depth to 38 inches (which we will also convert to feet):
38 inches * (1 foot / 12 inches) = 3.1667 feet

Now we can calculate the volume difference:
Volume difference = New volume - Current volume
Volume difference = 25 feet * 0.5 feet * (3.1667 feet - 2.9167 feet) = 25/8 cubic feet

Therefore, the correct answer is option b. 25/8 cubic feet, which represents the amount of water that must be let into the trough to raise the water depth.