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SAT Math : SAT Mathematics

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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:

$\textup{15.36 grams}$

$\textup{12.32 grams}$

$\textup{4.34 grams}$

$\textup{17.12 grams}$

$\textup{6.51 grams}$

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 #851 : Sat Mathematics

Find the volume of the figure.

Possible Answers:

2036.33

2073.45

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 #42 : Cylinders

Find the volume of the figure.

Possible Answers:

100658.51

116992.91

112551.20

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 #161 : Solid 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:

$6\: \text{min}$

$3\: \text{min}$

$8\: \text{min}$

$5\: \text{min}$

$11\: \text{min}$

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 #34 : New Sat Math Calculator

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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Example Question #1 : Cylinders

An upright cylinder with a height of 30 and a radius of 5 is in a big tub being filled with oil. If only the top 10% of the cylinder is visible, what is the surface area of the submerged cylinder?

Possible Answers:

345π

295π

270π

300π

325π

Correct answer:

295π

Explanation:

The height of the submerged part of the cylinder is 27cm. 2πrh + πr²is equal to 270π + 25π = 295π

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Example Question #1 : Cylinders

A right circular cylinder has a height of 41 in. and a lateral area (excluding top and bottom) 512.5π in². What is the area of its bases?

Possible Answers:

None of the other answers

312.5 in²

78.125π in²

156.25 in²

39.0625π in²

Correct answer:

78.125π in²

Explanation:

The lateral area (not including its bases) is equal to the circumference of the base times the height of the cylinder. Think of it like a label that is wrapped around a soup can. Therefore, we can write this area as:

A = h * π * d or A = h * π * 2r = 2πrh

Now, substituting in our values, we get:

512.5π = 2 * 41*rπ; 512.5π = 82rπ

Solve for r by dividing both sides by 82π:

6.25 = r

From here, we can calculate the area of a base:

A = 6.25²π = 39.0625π

NOTE: The question asks for the area of the bases. Therefore, the answer is 2 * 39.0625π or 78.125π in².

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Example Question #1 : How To Find The Surface Area Of A Cylinder

The diameter of the lid of a right cylindrical soup can is 5 in. If the can is 12 inches tall and the label costs $0.00125 per square inch to print, what is the cost to produce a label for a can? (Round to the nearest cent.)

Possible Answers:

$0.24

$0.16

$0.29

$0.08

$1.18

Correct answer:

$0.24

Explanation:

The general mechanics of this problem are simple. The lateral area of a right cylinder (excluding its top and bottom) is equal to the circumference of the top times the height of the cylinder. Therefore, the area of this can's surface is: 5π * 12 or 60π. If the cost per square inch is $0.00125, a single label will cost 0.00125 * 60π or $0.075π or approximately $0.24.

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SAT Math : SAT Mathematics

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 #161 : Solid Geometry

Example Question #34 : New Sat Math Calculator

Example Question #1 : Cylinders

Example Question #1 : Cylinders

Example Question #1 : How To Find The Surface Area Of A Cylinder

All SAT Math Resources

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