a round silo is 60 ft tall and has a 18 ft radius. how high would a load of 32000 cubic ft of the grain fill
V=πr2h
V = 3.14 * 18^2 * 60
v = ______ cubic feet\\
To find out how high a load of 32000 cubic feet of grain would fill the round silo, we need to determine the volume occupied by the given height.
The formula to calculate the volume of a cylinder, such as a round silo, is V = πr^2h, where V represents volume, π (pi) is a mathematical constant (approximately 3.14), r is the radius, and h is the height.
Let's plug in the given values:
Radius (r) = 18 ft
Height (h) = ?
We have the volume (V) as 32000 cubic ft.
Using the volume formula, we can rearrange it to solve for the height (h):
V = πr^2h
32000 = 3.14 * (18^2) * h
32000 = 3.14 * 324 * h
32000 = 1017.36 * h
Now, to solve for h, we divide both sides of the equation by 1017.36:
h = 32000 / 1017.36
h ≈ 31.5 ft
Therefore, a load of 32000 cubic feet would fill approximately 31.5 ft of the round silo.
To determine how high a load of 32000 cubic feet of grain would fill a round silo, we need to calculate the volume of the silo and then divide the total volume by the volume of the grain load.
The volume of a cylinder (such as a silo) is given by the formula: V = πr^2h, where V represents the volume, r is the radius, and h is the height.
Given:
Height of the silo (h) = 60 ft
Radius of the silo (r) = 18 ft
Volume of the grain load = 32000 cubic ft
Now, let's calculate the volume of the silo:
V_silo = πr^2h
= π * (18 ft)^2 * 60 ft
= 97280π cubic ft (approximately 30519.16 cubic ft)
Next, we can determine the height the load of 32000 cubic ft of grain would fill in the silo:
Height_filled = Volume_of_grain_load / (πr^2)
= 32000 cubic ft / (π * (18 ft)^2)
≈ 32000 / (324π) ft
≈ 32000 / 1017.879 ft (rounded to 4 decimal places)
≈ 31.4526 ft (rounded to 4 decimal places)
Therefore, a load of 32000 cubic ft of grain would fill the round silo up to approximately 31.4526 ft high.