SOLUTION: Mrs. Moser wants a patio in the shape of a half-circle with a flat side of 16ft. How much concrete, to the nearest hundreth of a cubic yard, will she need if the patio slab is to b
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Question 1137050: Mrs. Moser wants a patio in the shape of a half-circle with a flat side of 16ft. How much concrete, to the nearest hundreth of a cubic yard, will she need if the patio slab is to be 4 inches thick? Found 2 solutions by Alan3354, Theo:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Mrs. Moser wants a patio in the shape of a half-circle with a flat side of 16ft. How much concrete, to the nearest hundreth of a cubic yard, will she need if the patio slab is to be 4 inches thick?
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Find the area of the half-circle
r = 8 ft
Area = pi*r^2 sq ft
Volume = area*h = area*(4/12) cu ft.
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1 cubic yard = 27 cu ft
You can put this solution on YOUR website! the patio will form half of a cylinder that has a diameter of 8 feet and a depth of 1/3 of a foot because 4 inches = 1/3 of a foot.
the volume of a cylinder is equal to pi * r^2 * h
r is the radius and h is the height.
since the radius is half the diameter, the radius is 8 feet.
the volume of the cylinder is pi * 8^2 * 1/3 = 67.02064328 cubic feet.
half of that is 33.51032164 cubic feet.
there are 27 cubic feet in 1 cubic yard.
therefore the volume of the patio will be 33.51032164 / 27 = 1.241123024 cubic yards.
mrs. moser will need 1.24 cubic yards of concrete to the nearest 100th of a cubic yard.
