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 1092246: 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 Boreal(15235) (Show Source): You can put this solution on YOUR website!
Will start with cubic inches: height is 89 inches and radius is 30 inches, half of 5 feet.
pi*30^2*89 is the in^3 volume, or 251,514 in^3.
There are 1728 in^3 for 1 ft^3, 12^3.
Therefore, there are 145.55 ft^3.
When there are 32 inches of feed in it, that is 32/89 of the total volume, or 52.33 ft^3. That means she needs 145.55-52.33 or 93.22 ft^3 of feed.
1 foot is 0.3048 m
1 meter is 1/.3048 or 3.28 feet
1 m^3 is 3.28 ft ^3, or 35.29 ft^3.
93.22 needed/35.29 ft^3 per m^3 is 2.64 m^3.
17.6 or 18 bags (2.64/0.15=17.6) will fill the container to capacity.
Check
Use feet as 7.417 tall with radius of 2.5 feet
pi*6.25*7.417=145.56, so the original volume is correct.
2 feet 8 inches is almost 1/3 of 7 feet 5 inches, so about 2/3 of the feeder should be filled, which is about 2/3 of about 150 ft^3 or about 100 ft^3, which is a little high.

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