PSAT Math : How To Find The Volume Of A Cylinder - Varsity Tutors

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We are open Saturday and Sunday! Call Now to Set Up Tutoring: (888) 888-0446 * Name Subject (optional) Create Problem Set PSAT Math : How to find the volume of a cylinder

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Example Questions

← Previous 1 2 3 Next → PSAT Math Help » Geometry » Solid Geometry » Cylinders » How to find the volume of a cylinder

Example Question #21 : Cylinders

What is the volume of a cylinder with a diameter of 13 inches and a height of 27.5 inches?

Possible Answers:

 

Correct answer:

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

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Example Question #311 : Geometry

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?

Possible Answers:

Correct answer:

Explanation:

Six inches is equal to 0.5 feet, so the height of the interior of the tank is

 feet;

the radius of the base of the interior of the tank is

 feet.

The amount of water the tank holds is the volume of the interior of the tank, which is

 cubic feet.

This rounds to 16,200.

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Example Question #22 : How To Find The Volume Of A Cylinder

The above diagram is one of a cylindrical tub. The company wants to make a cylindrical tub with four times the volume, but whose base is only three times the radius. How high should this new tub be?

Possible Answers:

Correct answer:

Explanation:

The volume of the given tub can be expressed using the following formula, setting  and ,

 cubic inches.

The new tub should have four times this volume, or

 cubic inches.

The radius is to be three times that of the above tub, which will be 

 inches.

The height can therefore be calculated as follows:

 inches

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Example Question #24 : How To Find The Volume Of A Cylinder

The above diagram is one of a cylindrical tub. The tub is holding water at 70% capacity. To the nearest cubic foot, how much more water can it hold?

Possible Answers:

Correct answer:

Explanation:

The volume of the cylinder can be calculated using the following formula, setting  and ,

 cubic inches.

The tub is 70% full, so it is 30% empty; it can hold

 more cubic inches of water.

The problem asks for the number of cubic feet, so divide by the cube of 12, or 1,728:

The correct response is 14 cubic feet.

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Example Question #25 : How To Find The Volume Of A Cylinder

Possible Answers:

Correct answer:

Explanation:

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Example Question #21 : Cylinders

Two cylinders are full of milk.  The first cylinder is 9” tall and has a base diameter of 3”.  The second cylinder is 9” tall and has a base diameter of 4”.  If you are going to pour both cylinders of milk into a single cylinder with a base diameter of 6”, how tall must that cylinder be for the milk to fill it to the top?

Possible Answers:

5"

9"

12"

6.25"

30"

Correct answer:

6.25"

Explanation:

Volume of cylinder = π * (base radius)2 x height = π * (base diameter / 2 )2 x height

Volume Cylinder 1 = π * (3 / 2 )2 x 9 = π * (1.5 )2 x 9 =  π * 20.25

Volume Cylinder 2 = π * (4 / 2 )2 x 9 = π * (2 )2 x 9 =  π * 36

Total Volume =  π * 20.25 + π * 36

Volume of Cylinder 3 = π * (6 / 2 )2 x H = π * (3 )2 x H = π * 9 x H

Set Total Volume equal to the Volume of Cylinder 3 and solve for H

π * 20.25 + π * 36 = π * 9 x H

20.25 + 36 = 9 x H

H = (20.25 + 36) / 9 = 6.25”

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