GRE Math : Geometry

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Example Questions

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

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

Possible Answers:

$12\pi$

$15\pi$

$4\pi$

$10\pi$

$42\pi$

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 #1 : Cylinders

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

Possible Answers:

$32\pi$

$100\pi$

$96\pi$

$64\pi$

$128\pi$

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 #3 : 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 A is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity B is greater.

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 #1 : Cylinders

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

Possible Answers:

256π

16π

none of these

128π

64π

Correct answer:

256π

Explanation:

circumference = πd

d = 2r

volume of cylinder = πr²h

r = 8, h = 4

volume = 256π

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

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:

$54\pi$

432

108

$108\pi$

$432\pi$

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:

$384\pi\:in^3$

$528\pi\:in^3$

$768\pi\:in^3$

$1536\pi\:in^3$

$892\pi\:in^3$

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 #11 : Solid Geometry

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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Example Question #314 : Geometry

Kate wants to paint a cylinder prism.

What is the surface area of her prism if it is inches tall and has a diameter of inches? Round to the nearest whole number.

Possible Answers:

70in^2

70.7in^2

43in^2

71in^2

Correct answer:

71in^2

Explanation:

First, find the area of the base of the cyclinder:

$\pi r^2=\pi(1.5)^2=2.25\pi$ and multiply that by two, since there are two sides with this measurement: $2.25\pi\cdot2=4.5\pi$ .

Then, you find the width of the rectangular portion (label portion) of the prism by finding the circumference of the cylinder:

$\pi\cdot d=\pi\cdot3=3\pi$ . This is then multiplied by the height of the cylinder to find the area of the rectanuglar portion of the cylinder: $3\pi\cdot6=18\pi$ .

Finally, add all sides together and round: $4.5\pi+18\pi=70.7=71in^2$ .

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Example Question #2 : How To Find The Surface Area Of A Prism

Prism_1_454590 This triangular prism has a height of feet and a length of feet.

What is the surface area of the prism? Round to the nearest tenth.

Possible Answers:

90ft^2

80ft^2

81ft^2

80.7 ft^2

Correct answer:

80.7 ft^2

Explanation:

Find the area of the triangular sides first:

$\frac{b\cdot h}{2}=\frac{3\cdot3}{2}=\frac{9}{2}=4.5.$

Since there are two sides of this area, we multiply the area by 2:

$4.5\cdot 2=9.$

Next find the area of the rectangular regions. Two of them have the width of 3 feet and a length of 7 feet, while the last one has a width measurement of $3\sqrt{2}$ feet and a length of 7 feet. Multiply and add all other sides:

$(3\cdot7)+(3\cdot7)+(3\sqrt2\cdot7)=21+21+21\sqrt2$ .

Lastly, add the triangular sides to the rectangular sides and round:

$9+21+21+21\sqrt2=80.7ft^2$ .

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Example Question #1 : How To Find The Volume Of A Prism

A rectangular prism has a width of 3 units, a length that is twice the width, and a height that is two-thirds the length. What is the volume of the prism?

Possible Answers:

units^3

Correct answer:

units^3

Explanation:

Remember, the formula for the volume of a rectangular prism is width times height times length:

$V=w\cdot h\cdot l$

Now, let's solve the word problem for each of these values. We know that W=3 . If length is double the width, then the length must be 6 units. If the height is two-thirds the length, then the height must be 4:

$6\cdot \frac{2}{3}=4$

Multiply all three values together to solve for the volume:

$V=w\cdot h\cdot l$

$V=3\cdot 4\cdot 6$

V = 72 units^3

The volume of the rectangular prism is units cubed.

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GRE Math : Geometry

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

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

Example Question #1 : Cylinders

Example Question #3 : How To Find The Surface Area Of A Cylinder

Example Question #1 : Cylinders

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

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

Example Question #11 : Solid Geometry

Example Question #314 : Geometry

Example Question #2 : How To Find The Surface Area Of A Prism

Example Question #1 : How To Find The Volume Of A Prism

All GRE Math Resources

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