A farm has two cylindrical silos for storing grain as shown.
How much greater is the volume, in cubic feet, of the larger silo than the smaller silo?
Use 3.14 for pi.
(3 points)
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The volume of Silo A is Response area ft3.
3
.
The volume of Silo B is Response area ft3.
3
.
The volume of Silo A is Response area cubic feet larger than the volume of the Silo B.
20,347.2
20
,
347.2
6,782.4
6
,
782.4
13,564.8
13
,
564.8
27,129.6
27
,
129.6
33,912.0
33
,
912.0
To calculate the volume of a cylindrical silo, we need to know the radius and height of each silo.
Let's denote the radius of the smaller silo as r1 and the radius of the larger silo as r2. We'll also denote the height of both silos as h.
The volume of a cylinder is given by the formula V = πr^2h.
The volume of Silo A is given as 20,347.2 ft^3, so we have the equation:
20,347.2 = π(r1)^2h
The volume of Silo B is given as 33,912.0 ft^3, so we have the equation:
33,912.0 = π(r2)^2h
Dividing the two equations, we get:
20,347.2 / 33,912.0 = (π(r1)^2h) / (π(r2)^2h)
Simplifying, we cancel out the π and h terms:
20,347.2 / 33,912.0 = (r1^2) / (r2^2)
Taking the square root of both sides:
sqrt(20,347.2 / 33,912.0) = (r1 / r2)
Simplifying:
sqrt(0.6) = (r1 / r2)
Therefore, the radius of Silo A is 0.7745966692 (approximately 0.775) times the radius of Silo B.
To find the volume ratio, we can use the formula V2 / V1 = (r2^2 * h) / (r1^2 * h)
As the height of both silos is the same, h cancels out:
V2 / V1 = r2^2 / r1^2 = (0.775)^2 / 1^2
V2 / V1 = 0.600625
Therefore, the volume of Silo A is approximately 60.1% of the volume of Silo B.
To find the volume difference between the two silos, we can subtract the volume of Silo A from the volume of Silo B:
Volume difference = Volume of Silo B - Volume of Silo A
Volume difference = 33,912.0 ft^3 - 20,347.2 ft^3
Volume difference = 13,564.8 ft^3
So, the volume of Silo A is 13,564.8 cubic feet smaller than the volume of Silo B.