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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 24 in24\,\text{in} and a base width of 15 in15\,\text{in}. The height of the water is 12 in12\,\text{in} above the base. During cleaning, 900 cubic inches900\,\text{cubic inches} of water is removed. What is the absolute value of the change in the height of the water in inches?\newline◻

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Q. A household aquarium tank in the shape of a rectangular prism has a base length of 24 in24\,\text{in} and a base width of 15 in15\,\text{in}. The height of the water is 12 in12\,\text{in} above the base. During cleaning, 900 cubic inches900\,\text{cubic inches} of water is removed. What is the absolute value of the change in the height of the water in inches?\newline◻
  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, the initial volume of water is: 2424 in ×\times 1515 in ×\times 1212 in.
  2. Find Initial Volume: Perform the multiplication to find the initial volume.\newline24 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 Remaining Volume: Calculate the volume of water in the tank after removing 900900 cubic inches.\newlineSince 900900 cubic inches of water is removed, we subtract this from the initial volume.\newline43204320 cubic inches −- 900900 cubic inches == 34203420 cubic inches.\newlineThis is the volume of water remaining in the tank.
  4. Calculate New Height: Calculate the new height of the water in the tank.\newlineWe use the formula for the volume of a rectangular prism again, but this time we solve for the height.\newlineThe new volume is 34203420 cubic inches, and the base area (length ×\times width) remains the same.\newlineSo, new height == new volume // (length ×\times width).\newlineNew height =3420= 3420 cubic inches // (2424 in ×15\times 15 in).
  5. Find New Height: Perform the division to find the new height.\newline34203420 cubic inches /(24/ (24 in ×15\times 15 in) = 34203420 cubic inches /360/ 360 square inches.\newlineNew height = 9.59.5 inches.\newlineThis is the height of the water after removing 900900 cubic inches.
  6. Calculate Change in Height: Calculate the absolute value of the change in the height of the water. The change in height is the initial height minus the new height. Change in height = 12 inches−9.5 inches=2.5 inches12\,\text{inches} - 9.5\,\text{inches} = 2.5\,\text{inches}. The absolute value of the change in height is ∣2.5 inches∣=2.5 inches|2.5\,\text{inches}| = 2.5\,\text{inches}.

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