SOLUTION: Chris bought a new grain bin that is a cylinder base with a cone top. The bin has a diameter of 19 ft. The height of the cylinder is 15 ft and the height of the cone is 6 ft. Cu

Algebra ->  Volume -> SOLUTION: Chris bought a new grain bin that is a cylinder base with a cone top. The bin has a diameter of 19 ft. The height of the cylinder is 15 ft and the height of the cone is 6 ft. Cu      Log On


   

Question 1037779: Chris bought a new grain bin that is a cylinder base with a cone top. The bin has a diameter of 19 ft. The height of the cylinder is 15 ft and the height of the cone is 6 ft. Currently, the oats that Chris wants to put into the bin is in a cone-shaped pile on the ground. The pile has a diameter of 40 ft and a height of 10.5 ft.
a. Find the volume of oats Chris has in the pile to the nearest cubic foot. hint: the pile is cone shaped.

b. Convert the volume of the oats in cubic feet to bushels.
Hint: 1 bu = 1.245 ft3


c. Find the capacity of the grain bin to the nearest cubic foot.


d. Find the capacity of the grain bin to the nearest bushel.
Hint: 1 bu = 1.245 ft3

e. Find the percent capacity to which the grain bin will be filled by the pile of oats.




Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Volume for a cylinder: pi%2Ar%5E2%2Ah, h is length top to bottom and r is radius. If let d be diameter, then d%2F2=r.

Volume for a cone: %281%2F3%29pi%2Ar%5E2%2Ah or %281%2F3%29pi%28d%2F2%29%5E2%2Ah, variables meaning same as used earlier although values may be different.

Only doing question part c.
Capacity of the grain bin:
%2815%2Api%2A%2819%2F2%29%5E2%2B6%2A%281%2F3%29pi%2A%2819%2F2%29%5E2%29%2AcubicFeet
15pi%2819%2F2%29%5E2%2B2pi%2819%2F2%29%5E2
%2815%2B2%29%28pi%2A%2819%2F2%29%5E2%29
17%2Api%2819%2F2%29%5E2
highlight%286137pi%2F4%29----------cubic feet, capacity of the grain bin.