A machine for baling hay produces cylindrical bales that are 5 feet in diameter and 4 1/3 feet in height. how many cubic feet are in each bale of hay?
To calculate the volume of a cylindrical bale, you need to use the formula for the volume of a cylinder, which is given by:
Volume = π * r^2 * h
Where:
- π is a mathematical constant approximately equal to 3.14
- r is the radius, which is half the diameter
- h is the height of the cylinder
Given that the diameter of the bale is 5 feet, the radius would be 5/2 = 2.5 feet. And the height is 4 1/3 feet, which can be converted to a mixed number (4 + 1/3) or an improper fraction (13/3).
So, we can substitute these values into the formula to calculate the volume:
Volume = π * (2.5)^2 * (13/3)
Now let's calculate it step-by-step.
Step 1: Calculate the square of the radius
Radius = 2.5
Radius^2 = (2.5)^2 = 6.25
Step 2: Calculate the volume using the formula
Volume = π * (2.5)^2 * (13/3)
Volume ≈ 3.14 * 6.25 * 13/3
Step 3: Simplify the expression
Volume ≈ 3.14 * 6.25 * 13/3
Volume ≈ 122.4 cubic feet
Therefore, each bale of hay has approximately 122.4 cubic feet of volume.
To find the volume of a cylindrical bale of hay, you need to use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius, and h is the height of the cylinder.
Given that the diameter of the bale is 5 feet, you can find the radius by dividing the diameter by 2. Therefore, the radius (r) is 5 feet divided by 2, which is 2.5 feet.
Next, convert the height of the bale from a mixed number to an improper fraction. The height is 4 1/3 feet, which can be written as 4 + 1/3 or 13/3 feet in improper fraction form.
Now you can calculate the volume using the formula:
V = πr^2h
V = 3.14 * (2.5)^2 * (13/3)
V = 3.14 * 6.25 * (13/3)
To simplify, multiply the numbers and divide where possible:
V ≈ 3.14 * 6.25 * (13/3)
V ≈ 3.14 * 125/3
V ≈ 392.5 cubic feet (rounded to one decimal place)
Therefore, each bale of hay has approximately 392.5 cubic feet.
V=Volume
A=Area
H=Height
D=Diameter
4 1/3 = 12/3 + 1/3 = 13/3
A=D^2*pi/4
V=A*H
V=(D^2*pi/4)*H
v=(5^2*pi/4)*13*3
V=25*pi*13/(3*4)
V=325*pi/12
V=325*3.14159/12
V=1021.01675/12
V=85.0847292 ft^3