GRE Math : GRE Quantitative Reasoning

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Example Questions

Example Question #1501 : Gre Quantitative Reasoning

What is the surface area of a cylinder with a radius of 6 and a height of 9?

Possible Answers:

96π

108π

64π

180π

225π

Correct answer:

180π

Explanation:

surface area of a cylinder

= 2πr² + 2πrh

= 2π * 6² + 2π * 6 *9

= 180π

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Example Question #2 : Solid Geometry

Quantitative Comparison

Quantity A: The volume of a cylinder with a radius of 3 and a height of 4

Quantity B: 3 times the volume of a cone with a radius of 3 and a height of 4

Possible Answers:

Quantity A is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity B is greater.

Correct answer:

The two quantities are equal.

Explanation:

There is no need to do the actual computations here to find the two volumes. The volume of a cone is exactly 1/3 the volume of a cylinder with the same height and radius. That means the two quantities are equal. The formulas show this relationship as well: volume of a cone = πr²h/3 and volume of a cylinder = πr²h.

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Example Question #1501 : Gre Quantitative Reasoning

A right circular cylinder of volume $200\pi$ has a height of 8.

Quantity A: 10

Quantity B: The circumference of the base

Possible Answers:

Quantity B is greater

The two quantities are equal

Quantity A is greater

The relationship cannot be determined from the information provided.

Correct answer:

Quantity B is greater

Explanation:

The volume of any solid figure is $base \times height$ . In this case, the volume of the cylinder is $200\pi$ and its height is , which means that the area of its base must be $25\pi$ . Working backwards, you can figure out that the radius of a circle of area $25\pi$ is . The circumference of a circle with a radius of is $10\pi$ , which is greater than .

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Example Question #1502 : Gre Quantitative Reasoning

What is the surface area of a cylinder that has a diameter of 6 inches and is 4 inches tall?

Possible Answers:

$4\pi$

$15\pi$

$42\pi$

$12\pi$

$10\pi$

Correct answer:

$42\pi$

Explanation:

The formula for the surface area of a cylinder is $\dpi{100} 2\pi r^{2}+ 2\pi rh$ ,

where is the radius and is the height.

$\dpi{100} SA=2\pi (3)^{2}+2\pi (3)(4)$

$\dpi{100} =42\pi$

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Example Question #311 : Geometry

A cylinder has a radius of 4 and a height of 8. What is its surface area?

Possible Answers:

$100\pi$

$128\pi$

$32\pi$

$96\pi$

$64\pi$

Correct answer:

$96\pi$

Explanation:

This problem is simple if we remember the surface area formula!

$SA = 2\pi r^2 +2\pi rh = 2\pi *16+2\pi *4*8 = 32\pi +64\pi = 96\pi$

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Example Question #4 : How To Find The Surface Area Of A Cylinder

Quantitative Comparison

Quantity A: Surface area of a cylinder that is 2 feet high and has a radius of 4 feet

Quantity B: Surface area of a box that is 3 feet wide, 2 feet high, and 4 feet long

Possible Answers:

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information given.

Correct answer:

Quantity A is greater.

Explanation:

Quantity A: SA of a cylinder = 2πr² + 2πrh = 2π * 16 + 2π * 4 * 2 = 48π

Quantity B: SA of a rectangular solid = 2ab + 2bc + 2ac = 2 * 3 * 2 + 2 * 2 * 4 + 2 * 3 * 4 = 52

48π is much larger than 52, because π is approximately 3.14.

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Example Question #2 : Cylinders

A cylinder has a height of 4 and a circumference of 16π. What is its volume

Possible Answers:

none of these

256π

64π

128π

16π

Correct answer:

256π

Explanation:

circumference = πd

d = 2r

volume of cylinder = πr²h

r = 8, h = 4

volume = 256π

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Example Question #1502 : Gre Quantitative Reasoning

Rusty is considering making a cylindrical grain silo to store his crops. He has an area that is 6 feet long, 6 feet wide and 12 feet tall to build a cylinder in. What is the maximum volume of grain that he can store in this cylinder?

Possible Answers:

$432\pi$

432

108

$108\pi$

$54\pi$

Correct answer:

$108\pi$

Explanation:

The maximum cylindrical base can have a diameter of 6 and therefore a radius of 3. The formula for the volume of a cylinder is $\dpi{100} \small \pi r^{2}h$ , which in this case is $\dpi{100} \small 3\times 3\times 12\times \pi$ .

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Example Question #2 : How To Find The Volume Of A Cylinder

A cylinder with volume of $192\pi\:in^3$ and a radius of $4\:in$ has its radius doubled. What is the volume of the new cylinder?

Possible Answers:

$892\pi\:in^3$

$528\pi\:in^3$

$768\pi\:in^3$

$384\pi\:in^3$

$1536\pi\:in^3$

Correct answer:

$768\pi\:in^3$

Explanation:

To begin, you must solve for the height of the original cylinder. We know:

$V=\pi r^2h$

For our values, we know:

$192\pi=\pi 4^2h=16\pi h$

Now, divide both sides by $16\pi$ :

12=h

So, if we have a new radius of , our volume will be:

$V=8^2*12*\pi=768\pi\:in^3$

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Example Question #1503 : Gre Quantitative Reasoning

If the dimensions of a rectangular crate are $6\times 7\times 8$ , which of the following CANNOT be the total surface area of two sides of the crate?

Possible Answers:

112

104

Correct answer:

Explanation:

Side 1: surface area of the 6 x 7 side is 42

Side 2: surface area of the 7 x 8 side is 56

Side 3: surface area of the 6 x 8 side is 48.

We can add sides 1 and 3 to get 90, so that's not the answer.

We can add sides 1 and 1 to get 84, so that's not the answer.

We can add sides 2 and 3 to get 104, so that's not the answer.

We can add sides 2 and 2 to get 112, so that's not the answer.

This leaves the answer of 92. Any combination of the three sides of the rectangular prism will not give us 92 as the total surface area.

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GRE Math : GRE Quantitative Reasoning

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1501 : Gre Quantitative Reasoning

Example Question #2 : Solid Geometry

Example Question #1501 : Gre Quantitative Reasoning

Example Question #1502 : Gre Quantitative Reasoning

Example Question #311 : Geometry

Example Question #4 : How To Find The Surface Area Of A Cylinder

Example Question #2 : Cylinders

Example Question #1502 : Gre Quantitative Reasoning

Example Question #2 : How To Find The Volume Of A Cylinder

Example Question #1503 : Gre Quantitative Reasoning

All GRE Math Resources

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