A round silo is 40 feet tall and has a 25 foot radius. How high would a load of 37000 cubic feet of grain fill the silo?
Express your answer rounded to the nearest foot.
V = pi*r^2*h.
37000 = 3.14*25^2*h, h = ?.
To find out how high the load of grain would fill the silo, we need to determine the volume the silo can hold and then calculate how much of that volume the load of grain occupies.
The volume of a cylinder (like a silo) can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given:
Height of silo (h) = 40 feet
Radius of silo (r) = 25 feet
Step 1: Calculate the volume of the silo
V = πr^2h
Plugging in the values:
V = π(25^2)(40)
V = π(625)(40)
V = 25000π cubic feet
Step 2: Calculate the height that the load of grain fills the silo
To find the height, we need to divide the volume of the grain by the area of the silo's base (πr^2) and then round to the nearest foot.
Height = Volume of grain / (πr^2)
Height = 37000 / (π(25^2))
Height = 37000 / (π(625))
Height ≈ 37000 / 1963.5
Height ≈ 18.84 feet
Rounding to the nearest foot, the load of 37000 cubic feet of grain would fill the silo to a height of approximately 19 feet.