SOLUTION: Please I need help 12th grade AP algebra, I tried several ways. Problem: A storage bin consists of a cylindrical section for storing grain, with a conical roof. The height of the r

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Question 818642: Please I need help 12th grade AP algebra, I tried several ways. Problem: A storage bin consists of a cylindrical section for storing grain, with a conical roof. The height of the roof is one-third of the total height and the radius is 10 feet. The volume of the storage bin is 1000 cubic feet. Find the height.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A storage bin consists of a cylindrical section for storing grain, with a conical roof.
The height of the roof is one-third of the total height and the radius is 10 feet.
The volume of the storage bin is 1000 cubic feet. Find the height.
:
Let x = the height of roof
then
2x = the height of the cylindrical section
and
3x = the total height
:
Cylinder Vol + Cone vol = 1000
pi%2A10%5E2%2A2x + 1%2F3pi%2A10%5E2%2Ax = 1000
pi%2A200x + 1%2F3pi%2A100x = 1000
Divide thru by 100
pi%2A2x + 1%2F3pi%2Ax = 10
multiply by 3 to get rid of the fraction
3%28pi%2A2x%29 + pi%2Ax = 30
6pi%2Ax%29 + pi%2Ax = 30
combine like terms
7pi%2Ax = 30
x = 30%2F%287pi%29
x = 1.364 ft is the height of the roof
3*1.364 ~4.1 ft is the height of the bin
:
This sounds kind of small, check it,
pi%2A10%5E2%2A2.73 = 857 cu/ft, cylindrical part
1%2F3pi%2An10%5E2%2A1.364 = 143 cu/ft cone part
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Total volume 1000 so guess it's right