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# Surface Area Word Problems Practice Questions

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Updated on Oct 3, 2011

To review these concepts, go to Surface Area Word Problems Study Guide.

## Surface Area Word Problems Practice Questions

### Practice 1

#### Problems

1. What is the surface area of a rectangular prism with a length of 15 cm, a height of 12 cm, and a width of 11 cm?
2. What is the surface area of a rectangular prism with a length of 20 m, a height of 21 m, and a width of 4 m?
3. What is the surface area of a cube with an edge of 9 in.?
4. The surface area of a cube is 96 m2. What is the length of an edge of the cube?

#### Solutions

1. Read and understand the question. This question is looking for the surface area of a rectangular prism. Each of the three dimensions is known.
2. Make a plan. Use the formula SA = 2lw + 2lh + 2wh, and substitute the given values for the length, width, and height.

Carry out the plan. The formula becomes SA = 2(15)(11) + 2(15)(12) + 2(11)(12).

Multiply to get SA = 330 + 360 + 264. Add to get a surface area of 954 cm2.

SA = 2(15)(11) + 2(15)(12) + 2(11)(12)

simplifies to

2(165) + 2(180) + 2(132) = 330 + 360 + 264 = 954

3. Read and understand the question. This question is looking for the surface area of a rectangular prism. Each of the three dimensions is known.
4. Make a plan. Use the formula SA = 2lw + 2lh + 2wh, and substitute the given values for the length, width, and height.

Carry out the plan. The formula becomes SA = 2(20)(4) + 2(20)(21) +2(4)(21). Multiply to get SA = 160 + 840 + 168. Add to get a surface area of 1,168 m2.

SA = 2(20)(4) + 2(20)(21) + 2(4)(21)

simplifies to

2(80) + 2(420) + 2(84) = 160 + 840 + 168 = 1,168

5. Read and understand the question. This question is looking for the surface area of a cube when the measure of the edge of the cube is given.
6. Make a plan. Use the formula SA = 6e2, and substitute the value of e. Remember that the surface area will be represented in square units.

Carry out the plan. Substitute into the formula to get SA = 6(9)2. Evaluate the exponent first to get SA = 6(81). Multiply to find the surface area: SA = 486 in.2.

486 ÷ 6 = 81

Then, take the positive square root of 81 to find the measure of the edge of the cube. The positive square root of 81 is 9, so this result is checking.

7. Read and understand the question. This question is looking for the measure of the edge of a cube when the total surface area is known.
8. Make a plan. Use the formula for the surface area of a cube and work backward to solve for e.

Carry out the plan. Substitute the values into the formula to get 96 = 6e2.

Divide each side of the equation by 6 to get 16 = e2. Take the positive square root of each side of the equation to find the value of e: e = 4 m.

Check your answer. To check this answer, substitute the value of e into the surface area formula. The formula becomes SA = 6(4)2. Evaluate the exponent to get SA = 6(16). Multiply to get a surface area of 96 m2. This result is checking.

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