Question

Concrete can be purchased by the cubic yard. How much will it cost to pour a circular slab 18 ft in diameter by 3 in. for a patio if the concrete costs $40.00 per cubic yard?

(1 cubic yard = 27 cubic feet)

Answer 1

The cost to pour a concrete slab for a patio that is 18 feet in diameter and 3 inches thick will be approximately $94.25, given that the concrete costs $40.00 per cubic yard.

Step-by-step explanation:

To calculate the cost of pouring a circular slab of concrete for a patio, which is 18 feet in diameter and 3 inches thick, with the concrete costing $40.00 per cubic yard, we must first find the volume of concrete needed in cubic feet and then convert it to cubic yards.

First, we calculate the area of the circle (A) using the formula A = πr², where r is the radius in feet (half of the diameter). Therefore, the radius is 18 ft / 2 = 9 ft.

A = π(9 ft)² = π * 81 ft² ≈ 254.47 ft².

Now, we need to consider the depth of the slab, which is 3 inches, or 0.25 ft (since there are 12 inches in a foot). The volume (V) of concrete required is the area multiplied by the depth.

V = 254.47 ft² * 0.25 ft = 63.6175 ft³.

To convert cubic feet to cubic yards, we divide by 27 (since there are 27 cubic feet in a cubic yard).

V = 63.6175 ft³ / 27 = ≈ 2.3562 cubic yards.

Finally, to find the cost, we multiply the number of cubic yards by the price per cubic yard:

Cost = 2.3562 cubic yards * $40/cubic yard = $94.25.

Therefore, it will cost approximately $94.25 to pour the concrete slab.

Answer 2

so hmmm check the picture below

now


`\bf V=\pi 9^2\cdot \cfrac{1}{4}\implies V=\cfrac{81\pi }{4} \\\\\\ \textit{there are }27ft^3\ in\ 1yd^3\textit{ thus, let's convert them to }yd^3 \\\\\\ \cfrac{(81\pi )/(4)}{27}\iff \cfrac{(81\pi )/(4)}{(27)/(1)}\implies \cfrac{81\pi }{4}\cdot \cfrac{1}{27}\implies \boxed{\cfrac{3\pi }{4}}`

now, that's how many yard³ are there for that slab, now, how much is the cost?

well, each yd³ costs $40, thus
`\bf 40\cdot \cfrac{3\pi }{4}`