410 Geometry

Geometry Practice Questions

1. What is the surface area, in square centimeters, of a cube with each edge length of 5 cm?

A. 15 B. 25C. 125D. 150

2. What is the surface area, in square centimeters, of a cylinder with a height of 10 cm and a radius of 6 cm?

A. 136πB. 160πC. 192πD. 256π

3. What is the surface area, in square centimeters, of a cylinder that measures 8 cm tall with a diameter of 6 cm on its base?

A. 48πB. 57πC. 66πD. 132π

4. A pyramid has a square base. If each edge of the pyramid is 4, what is the total surface area of the entire pyramid?

A. 8 3B. 8 3 16+C. 16 3 16+D. 64 3

Question 5 refers to the following figure.

16π

5. A toy factory paints all of its rubber balls with 2 coats of latex for durabil-ity. How many square centimeters of latex are needed to cover a rubber ball with a circumference of 16 cmπ ?

A. 64πB. 128πC. 256πD. 512π

6. The floor of a walk-in closet measures 7 feet by 4 feet. If the ceiling height is 8 feet, what is the volume in cubic feet of the closet?

A. 28 B. 56C. 112D. 224

Question 7 refers to the following figure.

10

3

7. An ice cream cone has a spherical scoop of ice cream placed inside. Exactly one-half of the ice cream is visible above the rim of the cone. What is the surface area of the entire ice cream treat, in units squared?

A. 24πB. 30πC. 48πD. 60π

8. The radius of Sphere A is 2, and the radius of Sphere B is 1. What is the ratio of the volume of Sphere A to that of Sphere B? (Hint: Use the formula for the volume of a sphere on page 398.)

A. 1:2B. 4:1C. 8:1D. 8:3

9. A parallelogram has a base of 6 centimeters and a height of 10 centimeters. This parallelogram has the same area as a triangle with a height of 5 centimeters. What is the measure, in centimeters, of the base of the triangle?

Write your answer in the box.

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Mathematical Reasoning 411

13. In a right triangle, the hypotenuse measures 15 inches. If one leg of the triangle measures 6 inches, which of the following equations could be used to find the length of the other leg (x) in inches?

A. 15 6x = −B. 15 6x = −C. 15 62 2 2x = +D. 15 62 2 2x = −

14. The length of a rectangle is three times its width. If the perimeter of the rectangle is 96 inches, what is its length in inches?

A. 12B. 24C. 36D. 48

Question 15 refers to the following figure.

7 cm

16π cm

15. Sarah is making party hats for a birthday party. Each hat is in the shape of a cone and will have a circumference of 16 cmπ and a slant height of 7 cm. She will be making 20 hats. What is the total surface area, in square centimeters, of all 20 hats combined?

A. 32πB. 56πC. 112πD. π1,120

Question 10 refers to the following figure.

18 in.

10. Three identical rectangular boxes are stacked one on top of another. The total height of all three boxes is the same as the width of one box. The length of the boxes is 18 in., and the width is half the length. What is the combined volume, in cubic inches, of all three boxes?

A. 1,458B. 1,800C. 2,124D. 3,136

11. Using a compass, Max hikes 300 yards due north of his campsite. From that point, he hikes 400 yards due east. If he were to hike directly to his campsite from this point, how many yards would he have to hike?

A. 400B. 500C. 600D. 700

12. The rectangular base of a container is 9 inches long and 7 inches wide. By how many cubic inches will the volume of the container increase if you increase the length of the base by 2 inches?

A. 84B. 126C. 168D. 216

9 in.

12 in.

7 in.

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412 Geometry

Question 19 refers to the following figures.

2 in.

3 in.

2 in.

3 in.

6 in.

3 in.

4 in.

4 in.

4 in.

19. Laura is painting model pyramids for an art project. She needs one tube of paint for every 30 square inches of surface area. If Laura paints each pyramid and its base, approximately how many tubes of paint should she buy?

A. 4B. 16C. 48D. 109

Answers and explanations begin on page 684.

Question 16 refers to the following figure.

2 in2 in.

16. Use your calculator to make the following calculation. In the figure above, a square con-tains a circle such that each of the sides of the square is touching a point on the circle. What is the area, in square inches, of the shaded portion?

A. 3.43B. 12.57C. 16.00D. 28.57

Questions 17 and 18 refer to the following.

A classroom is 40 feet long and 25 feet wide. The ceiling height is 12 feet. The school district plans to repaint the room and put in air-condi-tioning. The ceiling tile will not be painted.

17. What is the approximate total square foot-age of the four walls of the room? Ignore space taken up by windows and doors.

A. 1,200B. 1,560C. 1,920D. 4,000

18. To choose an air-conditioning system, the school district must know the volume of the room. What is the volume in cubic feet?

A. 1,000B. 3,120C. 12,000D. 15,625

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384 Equations, Inequalities, and Functions

Questions 6 and 7 refer to the following graph.

x

y

C

B

AD

6. If the graph of the equation y x 5= − − weredrawn on the grid, which of the points wouldbe on the line?

A. AB. BC. CD. D

7. If a line were drawn through points B and C,what would be the slope of the line?

A. 3−B. 1

3−

C. 13

D. 3

3. What is the equation of a line with a slope of4− that passes through the point (1, 2)?

A. y x4 2= − +B. y x4 6= − +C. y x4 1= +D. y x4 6= +

4. The ordered pair ( 2, 1)− − is a solution towhich of the following equations?

A. x y4 7− − =B. x y4 7+ = −C. x y4 7− = −D. x y4 7− + = −

Equations, Inequalities, and Functions Practice QuestionsDirections: You MAY use your calculator.

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13. What is the slope of a line that passesthrough the points (2, 4) and (4, 6)?

A. −2B. 1C. 2D. 4

15. What is the y-intercept of the line witha slope of 2 that passes through thepoint (1, 2)?

A. −2B. 1

2−

C. 0

D. 12

16. The graphs of the equations y x= + 3 and= −y x2 3− are drawn on a coordinate grid.

In the coordinate plane below, darken thecircle corresponding to the point at whichthe two lines intersect.

x

y

– 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6

1

2

3

4

5

6

–1

–2

– 3

– 4

– 5

– 6

20. The graph of which equation will passthrough points (0 −, 3) and (5, 7)?

A. 1x x= −32

B. y x= −2 3

C. y x= +2 7D. = −y x2 3+

385Mathematical Reasoning

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21.

B.

C.

D.

– 5 – 4 – 3

Which of the following graphs represents thesolution set of the inequality 2(x− −6) > 8 ?

A. (1)

(4)

–2 – 1 0 1 2 3 4 5

– 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5

– 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5

– 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5

Questions 22 and 23 refer to the following graph.

x

y

L

M

22. Which of the following ordered pairs showsthe location of point L?

A. ( 5− −, 1)B. −( 5, 1)C. −( 1, 5)D. (1 −, 5)

23. What is the slope of the line that passesthrough points L and M?

A. −32

B. 23

−

C.

D.

2332

26. A line goes through the points (0, 2) and(1, 3). What is the equation of the line?

= − 1 +xA. y 32

B. 1y x= + 22

C. y x= + 2D. y x= + 3

32. Point B is located halfway between −( 1, 5)and ( 1− −, 3) . Name the location of point B.

In the coordinate plane below, darken thecircle corresponding to the location ofpoint B.

x

y

– 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6

1

2

3

4

5

6

–1

–2

– 3

– 4

– 5

– 6