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SAT Math : How to find the volume of a cylinder

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Example Question #31 : How To Find The Volume Of A Cylinder

ABC Pipeworks manufactures a 12 foot copper alloy pipe that has an internal diameter of 0.76 inches and an external diameter of 0.88 inches. If two grams of copper are in every 3 cubic inches of pipe material. How many grams of copper are in this pipe?

Possible Answers:

$\textup{12.32 grams}$

$\textup{17.12 grams}$

$\textup{15.36 grams}$

$\textup{4.34 grams}$

$\textup{6.51 grams}$

Correct answer:

$\textup{15.36 grams}$

Explanation:

First convert all units to inches.

internal diameter: 0.76 inches

external diameter: 0.88 inches

length: 144 inches

You are going to need to subtract the interior volume of the empty space inside the pipe from the external volume of the of the pipe.

Copper pipe

$[(\pi \ast .44^2)-(\pi \ast.38^2)] (144)=$

(.61-.45)(144)=

$(.16)(144)=23.04\, in^3$

Now, we need to determine how many grams of copper are in the pipe.

$(23.04\, in^3)\left ( \frac{2\, grams}{3\, in^3} \right )=$

$15.36\, grams\, of\, copper$

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Example Question #112 : Solid Geometry

Find the volume of the figure.

Possible Answers:

2073.45

2036.33

2158.25

2200.94

Correct answer:

2073.45

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 8^2 \times 12=768\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 3^2 \times 12=108\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=768\pi-108\pi=660\pi=2073.45$

Make sure to round to places after the decimal.

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Example Question #113 : Solid Geometry

Find the volume of the figure.

Possible Answers:

1006.37

1225.22

1109.87

1206.37

Correct answer:

1206.37

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 6^2 \times 12=432\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 2^2 \times 12=48\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=432\pi-48\pi=384\pi=1206.37$

Make sure to round to places after the decimal.

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Example Question #29 : How To Find The Volume Of A Cylinder

Find the volume of the figure.

Possible Answers:

1099.56

1124.52

1025.86

1233.45

Correct answer:

1099.56

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 6^2 \times 10=360\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 1^2 \times 10=10\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=360\pi-10\pi=350\pi=1099.56$

Make sure to round to places after the decimal.

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Example Question #31 : How To Find The Volume Of A Cylinder

Find the volume of the figure.

Possible Answers:

100658.51

112551.20

116992.91

122445.73

Correct answer:

116992.91

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 34^2 \times 40=46240\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 15^2 \times 40=9000\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=46240\pi-9000\pi=37240\pi=116992.91$

Make sure to round to places after the decimal.

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Example Question #181 : Geometry

Jessica wishes to fill up a cylinder with water at a rate of gallons per minute. The volume of the cylinder is gallons. The hole at the bottom of the cylinder leaks out 0.5 gallons per minute. If there are gallons in the cylinder when Jessica starts filling it, how long does it take to fill?

Possible Answers:

$8\: \text{min}$

$6\: \text{min}$

$11\: \text{min}$

$5\: \text{min}$

$3\: \text{min}$

Correct answer:

$8\: \text{min}$

Explanation:

Jessica needs to fill up gallons at the effective rate of $1.5\:\text{gal/min}$ . $12\: \text{gal}$ divided by $1.5\: \text{gal/min}$ is equal to $8 \:\text{min}$ . Notice how the units work out.

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Example Question #111 : Solid Geometry

The figure below represents a cylinder with a smaller cylinder removed from its middle.

Find the volume of the figure.

Possible Answers:

1896.77

1884.96

1865.32

1850.36

Correct answer:

1884.96

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 8^2 \times 10=640\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 2^2 \times 10=40\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=640\pi-40\pi=600\pi=1884.96$

Make sure to round to places after the decimal.

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SAT Math : How to find the volume of a cylinder

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #31 : How To Find The Volume Of A Cylinder

Example Question #112 : Solid Geometry

Example Question #113 : Solid Geometry

Example Question #29 : How To Find The Volume Of A Cylinder

Example Question #31 : How To Find The Volume Of A Cylinder

Example Question #181 : Geometry

Example Question #111 : Solid Geometry

All SAT Math Resources

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