Geometry homework

Question

Todd has a round above ground pool. It has a diameter of 27’. When the pool is full the water is 52’ deep. Todd took the cover off and the pool depth is at 3’. How many gallons of water will Todd need to add to bring the pool up to 52’? ( 1 cubic foot=7.49052 gallons)

Answer 1

52" = 4 1/3 ft

4 1/3 ft - 3 ft = 1 1/3 ft

V = π(13.5)²(1 1/3) ft³

V = 763.4 ft²

g = (763.4 ft³)(7.49052 gal/ft³)

g = 5,7183.3

Answer 2

This is a volume of a cylinder problem. v=pi r² h.

The radius of the pool is 27/2 = 13.5

When the pool depth is at 3 feet, the volume is pi (13.5)² (3)= 1717.6658 cubic feet.

When the pool depth is 52 feet, the volume is pi (13.5)² (52) = 29772.8736 ft³.

Subtract the two answers: 29772.8736 - 1717.6658 = 28055.2078 -->this is how many additional cubic feet of water are needed to fill the pool.

We will now multiply 28055.2078 by 7.49052 (because 1 cubic foot=7.49052 gallons)

Our answer is: 210148.0951 gallons