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A household aquarium tank in the shape of a rectangular prism has a base length of 24 inches (in) and a base width of 15in. The height of the water is 12 in above the base. During cleaning, 900 cubic inches of water is removed. What is the absolute value of the change in the height of the water in inches?

A household aquarium tank in the shape of a rectangular prism has a base length of 2424 inches (in) and a base width of 15in 15 \mathrm{in} . The height of the water is 1212 in above the base. During cleaning, 900900 cubic inches of water is removed. What is the absolute value of the change in the height of the water in inches?

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Q. A household aquarium tank in the shape of a rectangular prism has a base length of 2424 inches (in) and a base width of 15in 15 \mathrm{in} . The height of the water is 1212 in above the base. During cleaning, 900900 cubic inches of water is removed. What is the absolute value of the change in the height of the water in inches?
  1. Calculate Initial Volume: Calculate the volume of water in the tank before removing any water.\newlineThe volume of a rectangular prism is given by the formula: Volume = length ×\times width ×\times height.\newlineHere, the length is 2424 inches, the width is 1515 inches, and the height of the water is 1212 inches.\newlineSo, Volume = 2424 in ×\times 1515 in ×\times 1212 in.
  2. Find New Volume: Perform the multiplication to find the initial volume.\newlineVolume = 24 in×15 in×12 in=4320 cubic inches24 \, \text{in} \times 15 \, \text{in} \times 12 \, \text{in} = 4320 \, \text{cubic inches}.\newlineThis is the volume of water in the tank before any water is removed.
  3. Calculate New Height: Subtract the volume of water removed from the initial volume.\newlineWe know that 900900 cubic inches of water is removed from the tank.\newlineSo, the new volume of water in the tank is 43204320 cubic inches −- 900900 cubic inches.
  4. Determine Change in Height: Perform the subtraction to find the new volume of water. New Volume = 43204320 cubic inches - 900900 cubic inches = 34203420 cubic inches. This is the volume of water in the tank after removing 900900 cubic inches.
  5. Calculate Absolute Change: Calculate the new height of the water in the tank.\newlineWe know the base area of the tank (length ×\times width) is 24 in×15 in=360 square inches24 \text{ in} \times 15 \text{ in} = 360 \text{ square inches}.\newlineTo find the new height, we divide the new volume by the base area.\newlineNew Height = New Volume / Base Area = 3420 cubic inches/360 square inches3420 \text{ cubic inches} / 360 \text{ square inches} \newlinePerform the division to find the new height of the water.\newlineNew Height = 3420 cubic inches/360 square inches=9.5 inches3420 \text{ cubic inches} / 360 \text{ square inches} = 9.5 \text{ inches}\newlineThis is the height of the water after removing 900 cubic inches900 \text{ cubic inches}.Calculate the change in the height of the water.\newlineThe change in height is the original height minus the new height.\newlineChange in Height = Original Height - New Height = 12 inches−9.5 inches12 \text{ inches} - 9.5 \text{ inches} \newlinePerform the subtraction to find the change in height.\newlineChange in Height = 12 inches−9.5 inches=2.5 inches12 \text{ inches} - 9.5 \text{ inches} = 2.5 \text{ inches}.\newlineThis is the change in the height of the water.

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