Cylinders
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PSAT Math › Cylinders
What is the volume of a cylinder with a diameter of 13 inches and a height of 27.5 inches?
Explanation
The equation for the volume of a cylinder is V = Ah, where A is the area of the base and h is the height.
Thus, the volume can also be expressed as V = πr2h.
The diameter is 13 inches, so the radius is 13/2 = 6.5 inches.
Now we can easily calculate the volume:
V = 6.52π * 27.5 = 1161.88π in3
What is the volume of a cylinder with a diameter of 13 inches and a height of 27.5 inches?
Explanation
The equation for the volume of a cylinder is V = Ah, where A is the area of the base and h is the height.
Thus, the volume can also be expressed as V = πr2h.
The diameter is 13 inches, so the radius is 13/2 = 6.5 inches.
Now we can easily calculate the volume:
V = 6.52π * 27.5 = 1161.88π in3
Claire's cylindrical water bottle is 9 inches tall and has a diameter of 6 inches. How many cubic inches of water will her bottle hold?
Explanation
The volume is the area of the base times the height. The area of the base is 
Claire's cylindrical water bottle is 9 inches tall and has a diameter of 6 inches. How many cubic inches of water will her bottle hold?
Explanation
The volume is the area of the base times the height. The area of the base is
A water tank takes the shape of a closed cylinder whose exterior has height 40 feet and a base with radius 12 feet; the tank is six inches thick throughout. To the nearest hundred, how many cubic feet of water does the tank hold?
Explanation
Six inches is equal to 0.5 feet, so the height of the interior of the tank is
the radius of the base of the interior of the tank is
The amount of water the tank holds is the volume of the interior of the tank, which is
This rounds to 16,200.
A water tank takes the shape of a closed cylinder whose exterior has height 40 feet and a base with radius 12 feet; the tank is six inches thick throughout. To the nearest hundred, how many cubic feet of water does the tank hold?
Explanation
Six inches is equal to 0.5 feet, so the height of the interior of the tank is
the radius of the base of the interior of the tank is
The amount of water the tank holds is the volume of the interior of the tank, which is
This rounds to 16,200.
A hollow prism has a base 12 in x 13 in and a height of 42 in. A closed, cylindrical can is placed in the prism. The remainder of the prism is then filled with gel, surrounding the can. The thickness of the can is negligible. Its diameter is 9 in and its height is one-fourth that of the prism. The can has a mass of 1.5 g per in3, and the gel has a mass of 2.2 g per in3. What is the approximate overall mass of the contents of the prism?
15.22 kg
139.44 g
973.44 g
11.48 kg
13.95 kg
Explanation
We must find both the can volume and the gel volume. The formula for the gel volume is:
Gel volume = Prism volume – Can volume
The prism volume is simple: 12 * 13 * 42 = 6552 in3
The volume of the can is found by multiplying the area of the circular base by the height of the can. The height is one-fourth the prism height, or 42/4 = 10.5 in. The area of the base is equal to πr_2. Note that the prompt has given the diameter. Therefore, the radius is 4.5, not 9. The base's area is: 4.52_π = 20.25_π_. The total volume is therefore: 20.25_π_ * 10.5 = 212.625_π_ in3.
The gel volume is therefore: 6552 – 212.625_π_ or (approx.) 5884.02 in3.
The approximate volume for the can is: 667.98 in3
From this, we can calculate the approximate mass of the contents:
Gel Mass = Gel Volume * 2.2 = 5884.02 * 2.2 = 12944.844 g
Can Mass = Can Volume * 1.5 = 667.98 * 1.5 = 1001.97 g
The total mass is therefore 12944.844 + 1001.97 = 13946.814 g, or approximately 13.95 kg.
A hollow prism has a base 12 in x 13 in and a height of 42 in. A closed, cylindrical can is placed in the prism. The remainder of the prism is then filled with gel, surrounding the can. The thickness of the can is negligible. Its diameter is 9 in and its height is one-fourth that of the prism. The can has a mass of 1.5 g per in3, and the gel has a mass of 2.2 g per in3. What is the approximate overall mass of the contents of the prism?
15.22 kg
139.44 g
973.44 g
11.48 kg
13.95 kg
Explanation
We must find both the can volume and the gel volume. The formula for the gel volume is:
Gel volume = Prism volume – Can volume
The prism volume is simple: 12 * 13 * 42 = 6552 in3
The volume of the can is found by multiplying the area of the circular base by the height of the can. The height is one-fourth the prism height, or 42/4 = 10.5 in. The area of the base is equal to πr_2. Note that the prompt has given the diameter. Therefore, the radius is 4.5, not 9. The base's area is: 4.52_π = 20.25_π_. The total volume is therefore: 20.25_π_ * 10.5 = 212.625_π_ in3.
The gel volume is therefore: 6552 – 212.625_π_ or (approx.) 5884.02 in3.
The approximate volume for the can is: 667.98 in3
From this, we can calculate the approximate mass of the contents:
Gel Mass = Gel Volume * 2.2 = 5884.02 * 2.2 = 12944.844 g
Can Mass = Can Volume * 1.5 = 667.98 * 1.5 = 1001.97 g
The total mass is therefore 12944.844 + 1001.97 = 13946.814 g, or approximately 13.95 kg.
A metal cylindrical brick has a height of 
Explanation
To find the final volume, we will need to subtract the volume of the hole from the total initial volume of the cylinder.
The volume of a cylinder is given by the product of the base area times the height: 
Find the initial volume using the given base area and height.
Next, find the volume of the hole that was drilled. The base area of this cylinder can be calculated from the radius of the hole. Remember that the height of the hole is only half the height of the block.
Finally, subtract the volume of the hole from the total initial volume.
A hollow prism has a base 5 in x 6 in and a height of 10 in. A closed, cylindrical can is placed in the prism. The remainder of the prism is then filled with gel around the cylinder. The thickness of the can is negligible. Its diameter is 4 in and its height is half that of the prism. What is the approximate volume of gel needed to fill the prism?
103.33 in3
187.73 in3
203.44 in3
249.73 in3
237.17 in3
Explanation
The general form of our problem is:
Gel volume = Prism volume – Can volume
The prism volume is simple: 5 * 6 * 10 = 300 in3
The volume of the can is found by multiplying the area of the circular base by the height of the can. The height is half the prism height, or 10/2 = 5 in. The area of the base is equal to πr_2. Note that the prompt has given the diameter. Therefore, the radius is 2, not 4. The base's area is: 22_π = 4_π_. The total volume is therefore: 4_π_ * 5 = 20_π_ in3.
The gel volume is therefore: 300 – 20_π_ or (approx.) 237.17 in3.