Question

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 6 feet 8 inches and that it has a diameter of 6 feet. Respond to each of the following items. What is the maximum capacity of the feed cylinder, assuming there is a flat top to the cylinder? Express your answer in cubic feet. [Hint: For a right circular cylinder, V = πr2h. Remember that the radius r is ½ 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 3 feet 2 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 0.2 m3. How many bags of feed must she purchase to fill the feed container to capacity?

Answer 1

1) radius of cylinder (r) = 6/2 =3 feet, height (h) = 6 feet 8 inches

1 inch = 0.083 feet, hence 8 inches = 0.67 feet

h = 6+0.67 = 6.67 feet

Maximum capacity = volume of container =

2) height of currently filled feed = 3 feet 2 inch = 3 + (2x0.083) = 3.166 = 3.167 feet(approximately)

Volumr of currently filled feed =

Feed to be purchased = total capacity - currently filled feed = 188.5 - 89.6 = 98.9 cubic feet

Since 1 foot = 0.305 meter,

1 cubic feet = 0.305 × 0.305 × 0.305 = 0.283 cubic meters

Hence, 98.9 cubic feet = 98.9 x 0.283 = 27.98

= 28 cubic meters(approximately)

Hence, she needs to purchase 28 cubic meters of feed to fill the container back to its capacity.

3) Capacity of one bag = 0.2

Quantity required to fill the container = 28

Let n number of bags be required. Thus,

n x 0.2 = 28

Hence, 140 bags of feed are required.