Question

Alright, fellow mates. I have one last 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?

Answer 1

Volume of a cylinder is the area of the base times the height. The area of the base here is the area of a circle with diameter 18 feet. The height is 3 inches. Making the problem a bit trickier is the need to convert all the units.

Area of the base is
\[A_b = \pi r^2 = \frac{\pi d^2}{4} = \frac{\pi(18 \text{ ft}* 1\text{ yard}/3\text{ ft})^2}{4} = 9\pi \text{ yard}^2\]

Answer 2

Volume of the cylinder is the area of the base * height
\[V = (9\pi \text{ yard}^2) * (3 \text{ in}) * (1 \text{ yard}/36 \text{ in}) =\frac{3\pi}{4} \text{ yard}^3 \]Multiply that by \($40.00/1\text { yard}^3\) to get the price in dollars (\(\pi \approx 3.14159\)).