A pile of gravel is conical in shape. If the diameter is approximately 6.8m and the height is 2.8m, what is the volume of gravel in the pile.
v = (1/3)pi(r^2)h
r = d/2
= 6.8/2
= 3.4
v = (1/3)pi(3.4^2)(2.8)
still don't get this formula could you show me how to get the answer in more details?
To calculate the volume of a conical pile, we can use the formula:
V = (1/3) * π * r^2 * h
Where:
V = Volume of the cone
π ≈ 3.14159 (Pi)
r = Radius of the base of the cone
h = Height of the cone
First, we need to calculate the radius (r) of the cone. The diameter (d) is given as 6.8 meters, so we can find the radius by dividing the diameter by 2:
r = d/2 = 6.8/2 = 3.4 meters
Now that we have the radius and height, we can calculate the volume of the cone:
V = (1/3) * π * r^2 * h
= (1/3) * 3.14159 * (3.4^2) * 2.8
= 3.14159 * (3.4^2) * 2.8 / 3
Let's calculate this value:
V ≈ 3.14159 * 11.56 * 2.8 / 3
≈ 3.14159 * 32.368 * 2.8 / 3
≈ 3.14159 * 90.5344 / 3
≈ 284.16132 / 3
≈ 94.72044 cubic meters
Therefore, the volume of gravel in the pile is approximately 94.72 cubic meters.