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An inch is a twelfth of a foot; the word inch comes from the Latin uncia-, meaning a twelfth.
I am assuming this is a circular pool. The answer is Pi r^2 which comes to 572.5SF
Your patio is (8x8)/6in = 10.66 cubic foot. The sand comes in 50 lb bags that cover 0.5 cubic foot so you will need 21.33 bags (round up to 22 or down to 21)
The square footage of a 12 x 12 room is 144 feet. Most carpet comes in 12 foot width or wider. If it is 12 foot wide you just need a 12 foot piece off the roll. If the carpet is wider, you still have to buy that width and will have some waste.
A cut throat flume that is 3 feet wide at the throat comes with a 9-foot length