SOLUTION: Mrs.Carmichael keeps organic feed for her horses located in a cylinder in her barn. The cylinder is filled from the top and the feed is dispensed at the bottom. Mrs.Carmichael know

Question 1092174: Mrs.Carmichael keeps organic feed for her horses located in a cylinder in her barn. The cylinder is filled from the top and the feed is dispensed at the bottom. Mrs.Carmichael knows that the height of the cylinder is 7 feet 5 inches and that it has a diameter of 5 feet. Respond to each of the following items.
What is the maximum amount of feed the feed cylinder contains assuming there is a flat top to the cylinder? [Hint: For a right circular cylinder, V = πr2h. Remember that the radius r is � of the diameter. You may use 3.14 to approximate π.]
Mrs. Carmichael has a tape on the outside of the container that indicates to her the approximate height of the feed within it. She reads that the height of the feed in the container is about 2 feet 8 inches. How much feed should she purchase for her horses to ensure the feed container is filled again to capacity? Express this amount in cubic meters.
Next, Mrs. Carmichael visits her local agricultural co-operative to purchase the necessary amount of feed. She finds that each bag of organic horse feed has a mass of 50 kilograms with a corresponding capacity of 0.15 m3. How many bags of feed must she purchase to fill the feed container to capacity?
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
height of cylinder: 89 inches
Radius (1/2 diameter): 30 inches
The flat top has no bearing on the volume of the cylinder.
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1) Maximum amount of feed - Volume:
V = πr2h
V = π30^2 x 89
= 2827.433 x 89
= 251641.57 cu. in. or 145.63 cubic feet
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2) How much more to fill the cylinder to capacity
V = πr2h
V = π30^2 x 32
= = 2827.433 x 32 = 90477.86 cu. inches = 1.483 m^3
Cylinder capacity . . . : 251641.57 cu. in.
Less current content . .: 90477.86 cu. in.
Amount needed to fill . : 161163.71 cu. in. = 2.641 m^3
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3) How much should she buy
Bag of feed: 0.15 m^3
needed: 2.641 m^3
To buy: 2.641/0.15 = 17.6 (she has 2 choices, buy 17 bags and leave a little space at the top of the cylinder or buy 18 bags and have some feed left over)

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