a cone shape pile as a base diameter of 24feet and is 7feet tall. find the volume of the sawdust pile
To find the volume of the sawdust pile in a cone shape, you can use the formula:
Volume = (1/3) * π * r^2 * h
where π is the mathematical constant (approximately 3.14159), r is the radius of the base, and h is the height of the cone.
Given that the base diameter is 24 feet, we can calculate the radius as half of the diameter:
Radius (r) = 24 feet / 2 = 12 feet
The height (h) of the pile is given as 7 feet.
Now, we can substitute these values into the volume formula:
Volume = (1/3) * 3.14159 * (12 feet)^2 * 7 feet
Simplifying the equation:
Volume = (1/3) * 3.14159 * 144 square feet * 7 feet
Volume = 3.14159 * 144 square feet * 7 feet / 3
Volume ≈ 602.87 cubic feet
Therefore, the volume of the sawdust pile is approximately 602.87 cubic feet.
To find the volume of the cone-shaped pile, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Where V is the volume, π is a mathematical constant approximately equal to 3.1416, r is the radius of the base, and h is the height of the cone.
In this case, the base diameter is given as 24 feet. To find the radius, we divide the diameter by 2:
r = 24 feet / 2 = 12 feet
The height of the cone is given as 7 feet.
Now we can substitute the values into the volume formula:
V = (1/3) * π * (12 feet)^2 * 7 feet
= (1/3) * 3.1416 * 144 feet^2 * 7 feet
≈ 3.1416 * 144 feet^2 * 7/3
≈ 3.1416 * 48 feet^2 * 7
≈ 469.44 cubic feet
So, the volume of the sawdust pile is approximately 469.44 cubic feet.
as with any cone,
v = π/12 d^2 h