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Answer :
The approximate height of the water in the hot tub when it is 1/4 full is 4.6 inches, after converting the volume from gallons to cubic inches and dividing by the base area of the hot tub.
To find the approximate height of the water in the hot tub when it is 1/4 full, we need to calculate the total volume of the hot tub in cubic inches and then use that to find the height when the tub is only 1/4 full.
First, convert gallons to cubic inches using the provided conversion: 1 gallon = 231 cubic inches.
Then, total volume of the hot tub in cubic inches when full is: 360 gallons times 231 cubic inches/gallon = 83,160 cubic inches.
When the hot tub is 1/4 full, the volume of water is 1/4 of the total volume:
83,160 cubic inches times 1/4 = 20,790 cubic inches.
The base area of the hottub is 76 inches times 60 inches = 4,560 square inches.
Finally, to find the height of water when the hot tub is 1/4 full: 20,790 cubic inches \/ 4,560 square inches ≈ 4.56 inches.
The approximate height of the water in the hot tub is 4.6 inches (rounded to one decimal place).
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