A round silo is 55 feet tall and has a 18 foot radius. How high would a load of 31000 cubic feet of grain fill the silo?
To find the height at which a load of 31000 cubic feet of grain would fill the silo, we need to calculate the volume of the silo and then determine the corresponding height.
First, let's find the volume of the silo. The formula for the volume of a cylindrical silo is:
V = πr²h
where V is the volume, π is a constant approximately equal to 3.14, r is the radius, and h is the height.
Given that the radius of the silo is 18 feet and the height is 55 feet, we can substitute these values into the formula:
V = π × 18² × 55
V = 3.14 × 324 × 55
V ≈ 56439.6 cubic feet
The volume of the silo is approximately 56439.6 cubic feet.
To find the height at which a load of 31000 cubic feet of grain would fill the silo, we can set up a proportion:
31000 / 56439.6 = x / 55
Solving for x, we have:
x = (31000 × 55) / 56439.6
x ≈ 30.24 feet
Therefore, a load of 31000 cubic feet of grain would fill the round silo to a height of approximately 30.24 feet.
v = pi r^2 h
so, find h when
pi*18^2 h = 31000