How many cubic feet of crushed stone do you need to cover a 24 foot circumference?

Answer 1

That depends on the depth of coverage. Let's say you wish to cover the area to a depth of two inches. That's pretty typical. First calculate the area of the circle, which is given by the formula A = (Pi)r2. For a calculation such as this, you can use 3.14 as the value of Pi. But you don't know the value of r, so you'll need to figure that out first using the formula for the circumference, which is C = 2(Pi)r. Solving for r, we get r = C/2(Pi) = 24/6.28 = 3.82 feet. Now, solving for A, we get A = 3.14 * (3.82)2 = 45.8 square feet. But you're not done yet. Two inches (the depth) is equal to 1/6 foot (because there are 12 inches to the foot). So, 45.8 * (1/6) = 7.64 cubic feet. So, you need 7.6 cubic feet of crushed rock or stone. But what if the stone is sold by the yard? (Actually, that's a cubic yard, but sellers just say "yard.") Since there are 27 cubic feet to the (cubic) yard, you need about 0.28 yards, which is a little over a quarter of a yard. But what if your seller sells the stone by the ton? Guh! One cubic foot of crushed rock weighs about 100 pounds. So, you'll need 764 pounds of the rock. Since there are 2000 pounds per ton, you'll need 0.38 ton, which is a bit over a third of a ton. The first step was to calculate the area. The given formula for area is dependent upon the radius. For this problem, however, the radius was not know; we were given the circumference, so we needed to derive the radius from the formula for circumference. But you could have determined the area directly from the circumference, because the two attribute are inextricably linked! We know that A = (Pi)r2 and C = 2(Pi)r. From the second equation, we know that r = C/2(Pi), which was mentioned above. We can therefore substitute C/2(Pi) into the area equation, which gives us A = (Pi)[C/2(Pi)]2 = (Pi)C2/4(Pi)2 = C2/4(Pi). So, if you know the circumference, you can calculate the area. In our problem here, A = 242/4(Pi) = 576/12.57 = 45.8 square feet, which is what we got above. So, try to keep this formula in mind: A = C2/4(Pi).

Answer 2

Give you a hint: If your space was 12 foot x 20 foot x 1 foot it would be 12x20x1 or 240 cubic feet. Since you are only covering 2inches it will be less.