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This printable supports Common Core Mathematics Standard HSG-GMD.A.3

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# Volume of Cylinders (Grades 11-12)

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## Volume of Cylinders

1.
A cylindrical cup is 3 inches in diameter and 6 inches high. It is filled with water, to a depth of 4 inches. Two identical metal cubes are dropped in to the water, resulting in the water level rising by $3/4$ of an inch. Given that the volume of the displaced water equals the volume of the cubes, what is the size of one of the metal cubes?
1. 0.5 inches cubed
2. 2.3 inches cubed
3. 1.6 inches cubed
4. 2.7 inches cubed
2.
A cylindrical grain silo is 60 feet tall and has a capacity of 18,850 $ft^3$. What is the diameter of the silo?
1. 20 ft
2. 25 ft
3. 18 ft
4. 42 ft
3.
A cup, which is 4 inches deep and 3.5 inches in diameter, is filled with water and then poured into a cup that is 6 inches deep and 2.5 inches in diameter. Which statement is correct?
1. The water will not all fit in the second cup.
2. The water will fit in the second cup with room to spare.
3. The water will fill the second cup exactly to the top.
4. There is not enough information to determine.
4.
The shaft of a screwdriver is 8 inches long and $3/8$ of an inch in diameter. What volume of steel is in the shaft?
1. .72 cubic inches
2. 1.88 cubic inches
3. .88 cubic inches
4. 1.03 cubic inches
5.
Jamal wants to fill a plastic tote with water. The tote measures 12" X 16" X 24" and the container he is using to carry the water is a cylindrical jug with a depth of 10" and a diameter of 6". What is the minimum number of trips Jamal needs to make with the jug will to fill the tote?
1. 13
2. 17
3. 19
4. 29
6.
A cylindrical air duct with a diameter of 26" can hold 155 $ft^3$ of air. How long is the duct?
1. 41 feet
2. 23 feet
3. 25 feet
4. 19 inches
7.
A cylindrical water tower has a diameter of 62' and can hold enough water to supply the small town for two days. The town uses an average of 15,724 $ft^3$ per hour. How tall is the water tower?
1. 250 ft
2. 100 ft
3. 87 ft
4. 125 ft
8.
A plastics company manufactures straight sections for water slides. Each finished section is the shape of half of a cylinder and is 72" long and 32" wide at the inside of the top lip. If the sections are made one inch thick how much plastic does each section require?
1. 4,645 cubic inches
2. 7,954 cubic inches
3. 3,506 cubic inches
4. 7,012 cubic inches
9.
A company which manufactures hockey pucks produces 5,000 pucks per week and consumes 20.5 cubic feet of rubber in the process. If the pucks are 1" thick, what is the diameter of each puck?
1. 1.5 in
2. 3 in
3. 0.036 in
4. 2.6 ft
10.
A bridge will be supported by 16 cylindrical concrete supports, each of which has a height of 12 meters and a circumference of 7 meters. How much concrete will be needed to create the supports for the bridge?
1. $2973 \ "m"^3$
2. $186 \ "m"^3$
3. $749 \ "m"^3$
4. $47 \ "m"^3$
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