Name: ______________________ Class: _________________ Date: _________ ID: A

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Geometry Spring Final Exam Practice

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. The city commission wants to construct a new street that connects Main Street and North Boulevard as shown in the diagram below. The construction cost has been estimated at $110 per linear foot. Find the estimated cost for constructing the street. (1 mile = 5280 ft)

a. $30,787 c. $3,431,061b. $580,800 d. $3,386,617

____ 2. A 25.5 foot ladder rests against the side of a house at a point 24.1 feet above the ground. The foot of the ladder is x feet from the house. Find the value of x to one decimal place.

a. 1.9 b. 7.0 c. 8.3 d. 10.1____ 3. A scuba diver has a taut rope connecting the dive boat to an anchor on the ocean floor. The rope is 110

feet long. The water is 55 feet deep. To the nearest tenth of a foot, how far is the anchor from a point directly below the boat?a. 95.3 ft c. 81.4 ftb. 123.0 ft d. 89.8 ft

____ 4. In a 45°-45°-90° triangle, the ratio of the length of the hypotenuse to the length of a side is _____.a. 1:1 b. 3 :1 c. 2 :1 d. 2:1

Name: ______________________ ID: A

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____ 5. The shorter leg of a 30°-60°-90° triangle is 8.5 feet long. Find the perimeter.a. 25.5 + 8.5 2

Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ ft c. 17 + 8.5 2

Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ ft

b. 17 + 8.5 3Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ ft d. 25.5 + 8.5 3

Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ ft

____ 6. The tangent of ∠B is _____.

a. 957

b. 9512

c. 7 95 d. 127

____ 7. Write cos B.

a. 2425

b. 725

c. 724

d. 247

____ 8. To find the height of a tower, a surveyor positions a transit that is 2 meters tall at a spot 95 meters from the base of the tower. She measures the angle of elevation to the top of the tower to be 32°. What is the height of the tower, to the nearest meter?a. 154 m b. 59 m c. 61 m d. 152 m

____ 9. What is x to the nearest hundredth? (not drawn to scale)

a. x = 16.66 b. x = 13.51 c. x = 11.15 d. x = 10.04

Name: ______________________ ID: A

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____ 10. Use the diagram to find cos x as a fraction in simplest form.

a. 1213

c. 512

b. 2 25

d. 513

____ 11. Find the missing angle and side measures of ΔABC, given that m∠A = 65°, m∠C = 90°, and CB = 15.a. m∠B = 25°, c = 16.6, b = 7b. m∠B = 155°, c = 16.6, b = 7.5c. m∠B = 155°, c = 16.6, b = 7d. m∠B = 25°, c = 16.1, b = 7

____ 12. Solve for x to the nearest degree.

a. 30 b. 63 c. 60 d. 27____ 13. Two legs of a right triangle have lengths 15 and 8. The measure of the smaller acute angle is _____.

a. ≈ 32.2° b. ≈ 17° c. ≈ 61.9° d. ≈ 28.1°____ 14. Which of the following is NOT enough information to solve a right triangle?

a. Two sidesb. One side length and one trigonometric ratioc. Two anglesd. One side length and one acute angle measure

Name: ______________________ ID: A

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____ 15. Find the number of vertices, faces, and edges for the figure below.

a. 6 vertices, 6 faces, 10 edges c. 7 vertices, 7 faces, 11 edgesb. 5 vertices, 6 faces, 10 edges d. 10 vertices, 6 faces, 6 edges

____ 16. The shaded area of the figure is a planar cross section of a sphere that has a radius of r centimeters. (The figure may not be drawn to scale.)

The cross section is perpendicular to a radius of the sphere and intersects the radius one-fourth of the way from the center of the sphere to its surface. If the radius of the sphere, r, is 14 centimeters, which is the best approximation of the area of the cross section? Use 3.14 as an approximation for π.a. 606 cm 2 b. 577 cm 2 c. 269 cm 2 d. 85 cm 2

Name: ______________________ ID: A

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____ 17. Find the surface area of the triangular prism.

a. 62,396.4 cm2 c. 1271.7 cm2

b. 2225.5 cm2 d. 635.9 cm2

____ 18. If all the angles in the faces of the polyhedron below are right angles, then its surface area is _____.

a. 1678 in. 2 b. 1794 in. 2 c. 4485 in. 2 d. 839 in. 2

____ 19. Find the surface area of the cylinder to the nearest square unit. Use π ≈ 3.14.

a. 153 m2 b. 480 m2 c. 960 m2 d. 89 m2

Name: ______________________ ID: A

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____ 20. The pyramid shown has a rectangular base and faces that are isosceles triangles. Find the total surface area to the nearest tenth.

a. 86.0 ft 2 c. 37.3 ft 2

b. 75.8 ft 2 d. 73.9 ft 2

____ 21. The surface area of the right cone shown is _____.

a. 44π in. 2 c. 16 33 π in. 2

b. 112π in. 2 d. 36π in. 2

____ 22. The box shown is a candy container with a square base and a pyramidal top. How many square inches of pasteboard are need to make the box, not counting any overlapping edges?

a. 96 square inches c. 92.5 square inchesb. 112 square inches d. 144 square inches

Name: ______________________ ID: A

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____ 23. An aquarium in a restaurant is a rectangular prism and measures 4.5 feet by 4 feet by 2 feet. What is the volume of the aquarium?a. 32 cubic feet c. 10.5 cubic feetb. 36 cubic feet d. 12.5 cubic feet

____ 24. Find the exact volume of a cylinder that has a height of 18 inches and a radius of 8 inches.a. 384π in 3 c. 1152π in 3

b. 288π in 3 d. 144π in 3

____ 25. Find the volume of the right triangular prism.

a. 210 m 3 c. 105 m 3

b. 31 m 3 d. 20.5 m 3

____ 26. The volume of the right prism is _____.

a. 30 13 ft 3 c. 120 ft 3

b. 10 13 ft 3 d. 60 ft 3

Name: ______________________ ID: A

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____ 27. The volume of the right circular cylinder is about _____.

a. 265.5 m 3 c. 1036.9 m 3

b. 326.7 m 3 d. 1061.9 m 3

____ 28. A saucepan is designed so that if the liquid in the pan has a depth of 3.5 inches, the saucepan holds 2 quarts. One quart is equivalent to exactly 57.75 cubic inches. What is the approximate radius of the interior of the saucepan? Assume it is cylindrical and use 3.14 as an approximation for π.a. 5.26 inches c. 3.24 inchesb. 10.50 inches d. 6.48 inches

____ 29. The pyramid shown has a rectangular base and faces that are isosceles triangles. Find its volume.

a. 80 ft 3 c. 34 ft 3

b. 240 ft 3 d. 384 ft 3

____ 30. The volume of the pyramid below is _____.

a. 126 ft 3 c. 126π ft 3

b. 195π ft 3 d. 378 ft 3

Name: ______________________ ID: A

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____ 31. Calculate the volume of the cone. Use π ≈ 3.14.

a. 26.17 m 3 c. 157 m 3

b. 50 m 3 d. 471 m 3

____ 32. A machinist drilled a conical hole into a cube of metal as shown. If the cube has sides of length 8 cm, what is the volume of the metal after the hole is drilled? Use π ≈ 3.14 and round to the nearest tenth.

a. 378.0 cm 3 c. 351.2 cm 3

b. 333.4 cm 3 d. 333.5 cm 3

____ 33. A pyramid-shaped puzzle exactly fits its cubic storage box. The space between the puzzle and the sides of the box is filled with a light-weight plastic foam to help protect the puzzle during shipping.

What is the volume of the foam?a. 171.50 cm 3 c. 240.10 cm 3

b. 228.67 cm 3 d. 114.33 cm 3

Name: ______________________ ID: A

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____ 34. Find the surface area of a sphere that has a diameter of 16 cm. Express your answer in terms of π.a. 256π cm 2 c. 1024π cm 2

b. 64π cm 2 d. 20483

π cm 3

____ 35. Find the volume of a sphere 4 ft in diameter. Use π ≈ 3.14 and round your answer to the nearest tenth.a. 16.7 ft 3 c. 33.5 ft 3

b. 18.8 ft 3 d. 25.1 ft 3

____ 36. The inside of an ice cream cone is filled with ice cream and has radius 6 cm and height 12 cm. Assuming that a half-scoop of ice cream is in the shape of a hemisphere, and that it fits perfectly on top of the cone (same radius), find the total volume of ice cream. Use 3.14 for π and round your answer to the nearest tenth.a. 904.3 cm 3 c. 1356.5 cm 3

b. 1808.6 cm 3 d. 881.0 cm 3

Short Answer

37. Find the altitude of an isosceles triangle with base 10 and congruent sides of length 9.

38. If EFGH is a rectangle, what is FH?

39. Find the value of x and y.

40. Find the value of x and y.

Name: ______________________ ID: A

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41. SHORT RESPONSE Write your answer on a separate piece of paper.

A 14-foot ladder is placed against the side of a building, forming a right triangle as shown in Figure 1 below. The bottom of the ladder is 8 feet from the base of the building. In order to increase the height to which the ladder reaches, the ladder is moved 5 feet closer to the base of the building as shown in Figure 2.

To the nearest foot, how much farther up the building does the ladder now reach? Show how you arrived at your answer. (The figures may not be drawn to scale.)

42. Find the value of x and y.

43. A baseball "diamond" is a square with a side length of 90 feet. How far is the throw from third base to first base? (Round your answer to one decimal place.)

Name: ______________________ ID: A

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44. Find the value of x.

45. Find tan S.

46. Find tan A for the right triangle below:

47. Explain how a tangent ratio can be used to find the height of the building in the figure below. Find the height of the building when ∠A = 35°.

Use a special right triangle to find the tangent of the given angle.

48. 30°

49. 45°

50. Write the trigonometric ratio.

a. cos Bb. tan Ac. sin B

Name: ______________________ ID: A

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51. A 220 ft string attached to a kite makes a 30 o angle with the ground. What is the height of the kite to the nearest tenth?

Solve the right triangle:

52. α = 50 o and a = 10; find β, b, and c

Find the measure of an acute angle that satisfies the given equation. Round your answers to the nearest tenth of a degree.

53. tan Y = 940

54. sin X = 711

55. The shaded area in the figure is a planar cross section of the pyramid. The pyramid's edges are all 16 centimeters long and the base of the pyramid is a square. (The figure may not be drawn to scale.)

What is the perimeter of the cross section? Round your answer to the nearest tenth of a centimeter.

Name: ______________________ ID: A

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56. Find the surface area of the right prism.

57. Johannas is building a square sandbox with sides 3 feet long. He wants to put sand 1.05 feet deep in the box. How many cubic feet of sand should Johannas order?

58. Find the volume of a cylinder with height 9.7 km and diameter 20 km. Use π ≈ 3.14.

59. The pyramid shown has a rectangular base and faces that are isosceles triangles. Find its volume.

60. Find the volume of a right cone with slant height of 97 cm and radius of 65 cm. Express in terms of π.

Name: ______________________ ID: A

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Find the volume of the figure to the nearest tenth.

61.

62. Find the diameter of a sphere that has a surface area of 169π in 2 .

63. A sphere fits snugly inside a right cylinder as shown below. Find the volume lying outside the sphere but inside the cylinder to the nearest tenth of a cubic inch.

64. In the triangle, the measure of altitude RS is 24.

a. Find PQ to the nearest tenth of a unit.

b. Find the perimeter of ΔPQR to the nearest whole number.

Name: ______________________ ID: A

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65. The regular pyramid shown has a square base, with an altitude that is the same length as a side of the base. (The figure may not be drawn to scale.)

Find the value of x, the slant height of the pyramid, in feet. Round your answer to the nearest hundredth of a foot.

66. Three balls are packaged in a cylindrical container as shown below. If the balls just touch the top, bottom, and sides of the cylinder, how much of the space inside the cylinder is not filled by the balls if the diameter of a single ball is 7 cm? Justify each step in your solution.

ID: A

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Geometry Spring Final Exam PracticeAnswer Section

MULTIPLE CHOICE

1. D 2. C 3. A 4. C 5. D 6. A 7. B 8. C 9. D 10. A 11. A 12. A 13. D 14. C 15. A 16. B 17. C 18. A 19. C 20. B 21. A 22. A 23. B 24. C 25. C 26. D 27. D 28. C 29. A 30. A 31. C 32. A 33. B 34. A 35. C 36. A

ID: A

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SHORT ANSWER

37. 56 or 2 14 38. 65 39. x = 11 2 , y = 11 + 11 3 or 11(1 + 3 )

40. x = 3 3 , y = 6

41. In Figure 1, the ladder reaches a height of 14 2 − 8 2 = 132 , or about 11.49 feet.

In Figure 2, the ladder reaches a height of 14 2 − 3 2 = 187 , or about 13.67 feet. To the nearest foot, the difference is 2 feet.

42. x = 13, y = 13 3 43. 127.3 ft 44. x = 4 2

45. 47

46. 815

47. Using the tangent ratio tan A =leg opposite ∠A

leg adjacent to ∠A, tan 35 o = h

150. So h = 150 tan 35 oÊ

ËÁÁÁÁ

ˆ

¯˜̃̃˜ ≈ 150 0.7( ) ,

or about 105 ft.

48. 33

49. 1

50. a. ac

b. ab

c. bc

51. 110.0 ft

52.

β = 40 o

b ≈ 8.39

c ≈ 13.05 53. m∠Y ≈ 12.7° 54. m∠X ≈ 39.5° 55. 54.6 centimeters 56. 4104 m 2

57. 9.45 ft 3

58. 3045.80 km3

59. 80 ft 3

60. 101,400π cm 3

61. 207.3 mm 3

62. 13 in.

ID: A

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63. 113

π in. 3 ≈ 11.5 in. 3

64. a. 55.7b. 130

65. 11.18 66. 269.4 cm 3