A 4inch-thick concrete slab is being poured for a circular patio 14 feet in diameter. Concrete costs $55 per cubic yard. Find the cost of the concrete, to the nearest cent.
This concrete slab is a cylinder with a height of 4 inches and a circular base with a 14 foot diameter.
Volume of cylinder = pi * radius^2 * h
Substitute the values given remembering to change 4 inches to 1/3 foot.
After you find the volume ( in cubic feet ) multiply by $55..
36 foot by 13 foot
To find the cost of the concrete, we need to calculate the volume of the circular patio and then multiply it by the cost per cubic yard of concrete.
1. Start by finding the volume of the circular patio. The formula for the volume of a cylinder is given by V = π * r^2 * h, where π is a mathematical constant approximately equal to 3.14159, r is the radius of the patio (half the diameter), and h is the thickness of the concrete slab.
Given:
Diameter = 14 feet
Radius (r) = Diameter / 2 = 14 / 2 = 7 feet
Thickness (h) = 4 inches = 4/12 = 1/3 feet
Therefore, the volume of the circular patio is V = 3.14159 * 7^2 * (1/3).
2. Use a calculator to compute the volume:
V ≈ 3.14159 * 49 * (1/3) ≈ 51.83591 cubic feet.
3. Convert the volume to cubic yards since the cost is given per cubic yard. There are 27 cubic feet in one cubic yard.
Volume in cubic yards = V / 27 ≈ 51.83591 / 27 ≈ 1.92022 cubic yards.
4. Finally, multiply the volume in cubic yards by the cost per cubic yard to find the total cost:
Cost = Volume in cubic yards * Cost per cubic yard = 1.92022 * $55 ≈ $105.62 (to the nearest cent).
Therefore, the cost of the concrete for the circular patio, to the nearest cent, is $105.62.