What is the diameter of a barrel that is 3.5 ft tall and holds 11 cubic feet of water
vol = πr^2 h
πr^2 (3.5) = 11
r^2 = 11/(3.5π)
r = √(11/(3.5π)) = appr 1
so the diameter is appr 2 ft
check:
Vol = π(1^2)(3.5) = 10.9955.. , OK!
To find the diameter of a barrel given its height and the amount of water it holds, you will need to use the formula to calculate the volume of a cylinder. The formula for the volume of a cylinder is:
V = π * r^2 * h
Where:
V is the volume
π is a mathematical constant approximately equal to 3.14159
r is the radius of the base of the cylinder
h is the height of the cylinder
In this case, you know the volume (11 cubic feet) and the height (3.5 ft). So, you can rearrange the formula to solve for the radius, and then double the radius to get the diameter.
Let's begin by substituting the known values into the formula:
11 = π * r^2 * 3.5
Now, isolate the radius:
r^2 = 11 / (π * 3.5)
r^2 ≈ 1.003
Next, find the square root of both sides:
r ≈ √1.003
r ≈ 1.0015
Finally, calculate the diameter by multiplying the radius by 2:
d ≈ 2 * 1.0015
d ≈ 2.003 feet
Therefore, the approximate diameter of the barrel is 2.003 feet.