Question

The inner dimensions of an in-ground swimming pool are: width = 13.0ft, length = 18.0 ft, and depth = 9.0ft. the pool walls and the bottom are uniformly 1.0 ft thick and made of concrete. what is the total concrete surface area of the pool in units of ft2?

Answer 1

In swimming pool, the area would be only 5 pieces of rectangles since the top would be open. But if each area needs 1ft thick of concrete, then the length and width will be increased 2ft, but height only increased 1 ft. Make it length=20ft, width= 15ft, height= 10ft
Then to find the swimming pool area that need to be put some concrete the formula is:

Swimming pool area= length x width+ 2(length x height) + 2 (width x height)
Swimming pool area= 20ft x 15ft+ 2(20ft x 10ft) + 2( 15ft x 10ft)= 300ft
`ft^(2)` + 600
`ft^(2)` + 300
`ft^(2)`= 1200
`ft^(2)`

Answer 2

The swimming pool is in the shape of a open top rectangular prism. The concrete boundary of the swimming pool is in the shape of rectangular prism slabs.

The surface area of the interior sides of the swimming pool is given by 2(13 x 9)ft + 2(18 x 9)ft = 234ft + 324ft = 558ft^2

The surface area of the interior bottom of the swimming pool is given by 13 x 18 = 234ft^2.

The surface area of the exterior sides of the swimming pool is given by 2(15 x 10)ft + 2(20 x 10)ft = 300ft + 400ft = 700ft^2

The surface area of the exterior bottom of the swimming pool is given by 15 x 20 = 300ft^2.

The surface area of the top thickness of the swimming pool is given by 2(1 x 14) + 2(1 x 19) = 28 + 38 = 66ft^2

Therefore, total surface area = 558 + 234 + 700 + 300 + 66 = 1,858 ft^2.