A 4-inch-thick concrete slab is being poured for a circular patio 10 feet in diameter. Concrete costs $50 per cubic yard. Find the cost of the concerte, to the nearest cent. Show how you come to your answer.

1 cubic yard is 27 cubic feet. SO, concrete costs about $1.85 per cubic foot.

A 4" slab is 1/3 foot thick. So, the volume of concrete is the area of the patio, times its thickness, all in feet:

v = pi * 25 * 1/3 = 26.18 cubic feet.

cost = 26.18 * 1.85 = $48.43

Makes sense, since it's almost 1 cubic yard.

To find the cost of the concrete, we need to determine the volume of the slab first.

The volume of a cylinder (which represents the concrete slab) can be calculated using the formula: V = πr²h,
where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius (half the diameter), and h is the height (thickness of the slab).

Given:
Diameter of the circular patio = 10 feet

Radius (r) of the circular patio:
r = diameter / 2
r = 10 ft / 2
r = 5 ft

Height (h) or the thickness of the concrete slab:
h = 4 inches = 4/12 ft (since 1 ft = 12 inches)
h = 1/3 ft

Now, we can substitute the values in the volume formula:
V = πr²h
V = 3.14159 * (5 ft)² * (1/3 ft)
V ≈ 26.1799 ft³ (rounded to four decimal places)

Next, we need to convert the volume from cubic feet to cubic yards since the concrete cost is given in dollars per cubic yard.

To convert from cubic feet to cubic yards, we divide the volume by 27 (since 1 cubic yard = 27 cubic feet):
Volume in cubic yards = Volume in cubic feet / 27
Volume in cubic yards ≈ 26.1799 ft³ / 27
Volume in cubic yards ≈ 0.9696 yd³ (rounded to four decimal places)

Finally, we can calculate the cost of the concrete:

Cost of concrete = Volume in cubic yards * Cost per cubic yard
Cost of concrete ≈ 0.9696 yd³ * $50
Cost of concrete ≈ $48.48

Therefore, the cost of the concrete, to the nearest cent, is approximately $48.48.