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

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?
--------
Find the area of the half-circle
r = 8 ft
Area = pi*r^2 sq ft
Volume = area*h = area*(4/12) cu ft.
----
1 cubic yard = 27 cu ft

Answer by Theo(13342) (Show Source): 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.

RELATED QUESTIONS
A patio in the shape of a half circle and is 4 inches thick is being built. The radius is (answered by stanbon,vleith)
Mindy is building a patio that is in the shape of a square. The patio will cover 56... (answered by stanbon)
Mindy is building a patio that is in the shape of a square. The patio will cover 56... (answered by solver91311)
Emma wants to start with a square patio and experiment with the sides to see how changing (answered by gonzo)
A 5-inch-thick concrete slab is being poured for a circular patio 20 feet in diameter.... (answered by Fombitz)
ISBN-0618372628 Determine the circumference of a circle with radius 3in. Give a... (answered by rchill)
Concrete is sold by the yard, which means by the cubic yard. It costs $70 per yard. How... (answered by checkley75)
could you please help me with this problem. this is for pre-calc. You are a... (answered by htmentor)
A patio needs to be painted. The shape of the patio is made up of a rectangle with a... (answered by Cromlix)