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

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) (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
+ = 1000
+ = 1000
Divide thru by 100
+ = 10
multiply by 3 to get rid of the fraction
+ = 30
+ = 30
combine like terms
= 30
x =
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,
= 857 cu/ft, cylindrical part

= 143 cu/ft cone part
--------------------------------
Total volume 1000 so guess it's right

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