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SAT Math : How to find the volume of a cylinder

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Example Questions

Example Question #151 : Solid Geometry

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:

$\textup{12.32 grams}$ $\displaystyle \textup{12.32 grams}$

$\textup{17.12 grams}$ $\displaystyle \textup{17.12 grams}$

$\textup{6.51 grams}$ $\displaystyle \textup{6.51 grams}$

$\textup{4.34 grams}$ $\displaystyle \textup{4.34 grams}$

$\textup{15.36 grams}$ $\displaystyle \textup{15.36 grams}$

Correct answer:

$\textup{15.36 grams}$ $\displaystyle \textup{15.36 grams}$

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

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

$\displaystyle (.61-.45)(144)=$

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

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

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

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

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Example Question #851 : Sat Mathematics

Find the volume of the figure.

Possible Answers:

2036.33 $\displaystyle 2036.33$

2073.45 $\displaystyle 2073.45$

2158.25 $\displaystyle 2158.25$

2200.94 $\displaystyle 2200.94$

Correct answer:

2073.45 $\displaystyle 2073.45$

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:

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

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

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

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

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

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

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

Make sure to round to $\displaystyle 2$ places after the decimal.

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Example Question #113 : Solid Geometry

Find the volume of the figure.

Possible Answers:

1006.37 $\displaystyle 1006.37$

1225.22 $\displaystyle 1225.22$

1109.87 $\displaystyle 1109.87$

1206.37 $\displaystyle 1206.37$

Correct answer:

1206.37 $\displaystyle 1206.37$

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:

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

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

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

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

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

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

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

Make sure to round to $\displaystyle 2$ 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 $\displaystyle 1099.56$

1124.52 $\displaystyle 1124.52$

1025.86 $\displaystyle 1025.86$

1233.45 $\displaystyle 1233.45$

Correct answer:

1099.56 $\displaystyle 1099.56$

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:

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

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

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

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

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

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

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

Make sure to round to $\displaystyle 2$ places after the decimal.

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Example Question #42 : Cylinders

Find the volume of the figure.

Possible Answers:

$\displaystyle 100658.51$

$\displaystyle 116992.91$

$\displaystyle 112551.20$

$\displaystyle 122445.73$

Correct answer:

$\displaystyle 116992.91$

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:

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

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

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

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

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

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

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

Make sure to round to $\displaystyle 2$ places after the decimal.

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Example Question #1361 : Concepts

Jessica wishes to fill up a cylinder with water at a rate of $\displaystyle 2$ gallons per minute. The volume of the cylinder is $\displaystyle 14$ gallons. The hole at the bottom of the cylinder leaks out 0.5 $\displaystyle 0.5$ gallons per minute. If there are $\displaystyle 2$ gallons in the cylinder when Jessica starts filling it, how long does it take to fill?

Possible Answers:

$11\: \text{min}$ $\displaystyle 11\: \text{min}$

$3\: \text{min}$ $\displaystyle 3\: \text{min}$

$8\: \text{min}$ $\displaystyle 8\: \text{min}$

$6\: \text{min}$ $\displaystyle 6\: \text{min}$

$5\: \text{min}$ $\displaystyle 5\: \text{min}$

Correct answer:

$8\: \text{min}$ $\displaystyle 8\: \text{min}$

Explanation:

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

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

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

Find the volume of the figure.

Possible Answers:

1896.77 $\displaystyle 1896.77$

1850.36 $\displaystyle 1850.36$

1865.32 $\displaystyle 1865.32$

1884.96 $\displaystyle 1884.96$

Correct answer:

1884.96 $\displaystyle 1884.96$

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:

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

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

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

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

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

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

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

Make sure to round to $\displaystyle 2$ 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 #151 : Solid Geometry

Example Question #851 : Sat Mathematics

Example Question #113 : Solid Geometry

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

Example Question #42 : Cylinders

Example Question #1361 : Concepts

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

All SAT Math Resources

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