GRE Math : How to find the surface area of a prism

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

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:

104

112

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 #2 : Prisms

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:

43in^2

70.7in^2

70in^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 #3 : Prisms

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

80.7 ft^2

81ft^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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GRE Math : How to find the surface area of a prism

Study concepts, example questions & explanations for GRE Math

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Example Questions

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

Example Question #2 : Prisms

Example Question #3 : Prisms

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