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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?

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A household aquarium tank in the shape of a rectangular prism has a base length of $24\,\text{in}$ and a base width of $15\,\text{in}$ . The height of the water is $12\,\text{in}$ above the base. During cleaning, $900\,\text{cubic inches}$ 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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Add and subtract integers: word problems

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Q. A household aquarium tank in the shape of a rectangular prism has a base length of

24\,\text{in}

and a base width of

15\,\text{in}

. The height of the water is

12\,\text{in}

above the base. During cleaning,

900\,\text{cubic inches}

of water is removed. What is the absolute value of the change in the height of the water in inches?

\newline

◻

Calculate Initial Volume: Calculate the volume of water in the tank before removing any water. $\newline$ The volume of a rectangular prism is given by the formula: Volume = length $\times$ width $\times$ height. $\newline$ Here, the length is $24$ inches, the width is $15$ inches, and the height of the water is $12$ inches. $\newline$ So, the initial volume of water is: $24$ in $\times$ $15$ in $\times$ $12$ in.
Find Initial Volume: Perform the multiplication to find the initial volume. $\newline$ $24 \, \text{in} \times 15 \, \text{in} \times 12 \, \text{in} = 4320 \, \text{cubic inches}$ . $\newline$ This is the volume of water in the tank before any water is removed.
Calculate Remaining Volume: Calculate the volume of water in the tank after removing $900$ cubic inches. $\newline$ Since $900$ cubic inches of water is removed, we subtract this from the initial volume. $\newline$ $4320$ cubic inches $-$ $900$ cubic inches $=$ $3420$ cubic inches. $\newline$ This is the volume of water remaining in the tank.
Calculate New Height: Calculate the new height of the water in the tank. $\newline$ We use the formula for the volume of a rectangular prism again, but this time we solve for the height. $\newline$ The new volume is $3420$ cubic inches, and the base area (length $\times$ width) remains the same. $\newline$ So, new height $=$ new volume $/$ (length $\times$ width). $\newline$ New height $= 3420$ cubic inches $/$ ( $24$ in $\times 15$ in).
Find New Height: Perform the division to find the new height. $\newline$ $3420$ cubic inches $/ (24$ in $\times 15$ in) = $3420$ cubic inches $/ 360$ square inches. $\newline$ New height = $9.5$ inches. $\newline$ This is the height of the water after removing $900$ cubic inches.
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 = $12\,\text{inches} - 9.5\,\text{inches} = 2.5\,\text{inches}$ . The absolute value of the change in height is $|2.5\,\text{inches}| = 2.5\,\text{inches}$ .

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