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

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #64 : Solid Geometry

David wants to paint the walls in his bedroom. The floor is covered by a  carpet.  The ceiling is  tall. He selects a paint that will cover  per quart and  per gallon. How much paint should he buy?

Possible Answers:

1 gallon and 2 quarts

1 gallon

3 quarts

2 gallons and 1 quart

1 gallon and 1 quart

Correct answer:

1 gallon and 2 quarts

Explanation:

Find the surface area of the walls: SAwalls = 2lh + 2wh, where the height is 8 ft, the width is 10 ft, and the length is 16 ft.

This gives a total surface area of 416 ft2. One gallon covers 300 ft2, and each quart covers 75 ft2, so we need 1 gallon and 2 quarts of paint to cover the walls.

Example Question #61 : Solid Geometry

A box is 5 inches long, 5 inches wide, and 4 inches tall. What is the surface area of the box?

Possible Answers:

Correct answer:

Explanation:

The box will have six total faces: an identical "top and bottom," and identical "left and right," and an identical "front and back." The total surface area will be the sum of these faces.

Since the six faces consider of three sets of pairs, we can set up the equation as:

Each of these faces will correspond to one pair of dimensions. Multiply the pair to get the area of the face.

Substitute the values from the question to solve.

Example Question #66 : Solid Geometry

What is the surface area of a rectangular brick with a length of 12 in, a width of 8 in, and a height of 6 in?

Possible Answers:

None of the answers are correct  

Correct answer:

Explanation:

The formula for the surface area of a rectangular prism is given by:

SA = 2LW + 2WH + 2HL

SA = 2(12 * 8) + 2(8 * 6) + 2(6 * 12)

SA = 2(96) + 2(48) + 2(72)

SA = 192 + 96 + 144

SA = 432 in2

216 in2  is the wrong answer because it is off by a factor of 2

576 in3 is actually the volume, V = L * W * H 

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