A cone-shaped pile of sawdust has a base diameter of 24 feet, and is 9 feet tall. Find the volume of the pile.
(area of base) * 1/3 * height
area of circle = pi * d^2 /
To find the volume of a cone, we can use the formula V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
First, let's find the radius of the base of the cone. The base diameter is given as 24 feet, so the radius is half of that, which is 24/2 = 12 feet.
Next, we can substitute the values into the formula:
V = (1/3)π(12^2)(9)
Simplifying,
V = (1/3)π(144)(9)
V = (1/3)π(1296)
Finally, we can calculate the volume:
V = (1/3)(3.14)(1296)
V = 1357.44 cubic feet
Therefore, the volume of the pile is approximately 1357.44 cubic feet.
To find the volume of a cone, you can use the formula V = (1/3)πr^2h, where V represents the volume, π is a mathematical constant equal to approximately 3.14159, r is the radius of the base, and h is the height of the cone.
In this case, the base diameter is given, but we need the radius. The radius is half of the diameter, so the radius (r) will be 24 feet / 2 = 12 feet.
Now we have all the values we need to calculate the volume:
V = (1/3) * π * 12^2 * 9
Calculating this expression step by step:
V = (1/3) * 3.14159 * 144 * 9
V = (1/3) * 3.14159 * 1296
V = 0.3333 * 3.14159 * 1296
V ≈ 1365.41 cubic feet
Therefore, the volume of the pile is approximately 1365.41 cubic feet.