SOLUTION: Farmer John stores grain in a silo. The silo is cylinder-shaped. It has one flat rectangular face that rests against the side of the barn. The height of the silo is 30 feet and

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Question 305431: Farmer John stores grain in a silo. The silo is cylinder-shaped. It has one flat rectangular face that rests against the side of the barn. The height of the silo is 30 feet and the face resting against the barn is 10 feet wide. If the barn is approximately 5 feet from the center of the silo, determine the capacity of the silo in cubic feet of grain.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Farmer John stores grain in a silo. The silo is cylinder-shaped.
It has one flat rectangular face that rests against the side of the barn.
The height of the silo is 30 feet and the face resting against the barn is 10 feet wide.
If the barn is approximately 5 feet from the center of the silo, determine the
capacity of the silo in cubic feet of grain.
:
Find the radius of the silo
r = sqrt%285%5E2+%2B+5%5E2%29
r = 7.07 ft
:
Find the area of the circular base ignoring the flat side for now
A = pi%2A7.07%5E2
A = 157 sq/ft
:
A right triangle is formed by the 10' side and the two radii
Remove this, that leaves the area of 3/4 of the base
.75(157) = 118 sq/ft
:
Add the area of the right triangle to this
A = 118 + .5*.5*10
A = 118 + 25
A = 143 sq/ft
:
Find vol of the 30 ft silo
V = 143 * 30
V = 4,290 cu/ft