Geometry Name: _____________________________________

Unit 4 Exam Review Sheet

1. Look at the figure below.

If the dot indicates the center of the circle, which equation must be true?

A) mA =1

2mB

B) mA =2mB

C) mA + mB = 180°

D) mA + mB = 90°

2. In Circle O, which angle is equal to 90°?

A) AOC

B) COE

C) ABC

D) OED

3. Which statement correctly identifies an element of Circle O?

A) BA is a chord.

B) BD is a radius.

C) CD is a diameter.

D) C is a central angle.

4. Name all chords that are drawn in Circle C.

A) , ,CS CV CU

B) SU

C) ,SU WT

D) , ,SU UV TW

5. Which of these angles is a central angle of the circle shown below?

A) PRV

B) SPT

C) PVR

D) VRQ

6. Which segment is not a radius of Circle P?

A) QS

B) PR

C) QP

D) PS

7. Which segment represents a radius of the circle below?

A) CD

B) AB

C) FE

D) FB

8. The diameter of Circle P shown below is 3.5 inches.

If Points A, B, C, D, and E are equally spaced, what is the approximate

arc length from A to B?

A) 15.4 inches

B) 7.7 inches

C) 4.4 inches

D) 2.2 inches

9. Which measurement is closest to the area of the shaded sector in the circle

shown below?

A) 12.56 square inches

B) 25.12 square inches

C) 50.24 square inches

D) 75.36 square inches

10. The radius of Circle A below is 21 millimeters and the measure of BAC

is 60°. What is the length of Arc BC, to the nearest millimeter?

A) 11 mm

B) 22 mm

C) 26 mm

D) 30 mm.

11. The windshield wiper blade on Julia’s car is 21 inches long. Each swipe of the

wiper makes an angle of 85 degrees as pictured below.

To the nearest inch, how far does the tip of the windshield wiper travel with each

swipe of the blade?

A) 21 inches

B) 30 inches

C) 31 inches

D) 33 inches

12. A sprinkler is set to water the section of lawn represented by the shaded region in

the circle below.

Which measurement is closest to the area of the lawn watered by this sprinkler?

A) 18 square feet

B) 64 square feet

C) 154 square feet

D) 256 square feet

13. Chord RS is a diameter of Circle Q as shown below.

If the measure of Arc RP = 130°, what is the measure of SQP?

A) 25°

B) 50°

C) 65°

D) 130

14. Quadrilateral ABCD is inscribed in Circle Z such that side AD is a diameter of

Circle Z as shown below.

If mACB = 33° and mCAD = 30° what is ?mBC

A) 27°

B) 54°

C) 63°

D) 117°

15. Megan wants to construct a circle that circumscribes Scalene Triangle ABC. Which construction should Megan use to find the

center of this circle?

A) construct the medians of the sides of the triangle

B) construct the altitudes of the sides of the triangle

C) construct the angle bisectors of the angles of the triangle

D) construct the perpendicular bisectors of the sides of the triangle

16. Martin wants to inscribe a circle in scalene Triangle ABC. Which construction method

can he use to find the center of the circle?

A) construct the altitudes to BC and .AB

B) construct the angle bisectors of A and B.

C) construct the perpendicular bisectors of AC and .BC

D) construct the angle bisector of C and the perpendicular bisector of .AC

17. The steps below indicate some of the steps necessary to construct a tangent line from a point outside a given circle to the circle.

The steps are not in order.

I. Construct the midpoint of l.

II. Draw an arc that intersects with the circle.

III. Draw a straight line, l, between the center of the circle to the given point outside the circle.

IV. Draw a line connecting the given point outside the circle to the point where the arc intersects the circle.

What is the correct order of the steps above?

A) III, II, I, IV

B) III, I, II, IV

C) III, IV, II, I

D) III, I, IV, II

18. Which of the following is NOT part of the construction of a tangent line to a given circle from a point outside the circle?

A) finding the radius of the circle

B) finding a perpendicular bisector

C) finding the midpoint of a line segment

D) drawing an arc that intersects with the given circle

19. To play a marble game, Jana drew a circle and a line segment tangent to the circle on the sidewalk. Which of the following

represents Jana’s drawing?

A) B) C) D)

20. Find the measure of arc AB given that the length of arc AB is 16.76 inches. Round to the

nearest degree.

A) 2 degrees

B) 120 degrees

C) 240 degrees

D) 1185 degrees

21. Find the radius of circle C.

A) 24.7

B) 49.4

C) 12.3

D) 53.1

22. You constructed the above pie graph. How much greater would the central angle for

mountain bicycles be than the measure of the central angle for youth bicycles?

A) 11 degrees

B) 39.6 degrees

C) 93.6 degrees

D) 133.2 degrees

23. Which equation represents a circle with a center of (–3, 5) and a radius of 7?

A) (x – 3)2 + (y + 5)2 = 7 B) (x + 3)2 + (y – 5)2 = 7 C) (x – 3)2 + (y + 5)2 = 49 D) (x + 3)2 + (y – 5)2 = 49

24. The center of a circle is located at (8, –7) and has a radius of 4 units. Which equation represents this circle?

A) (x – 8)2 + (y + 7)2 = 16 B) (x + 8)2 + (y – 7)2 = 16 C) (x + 8)2 + (y – 7)2 = 4 D) (x – 8)2 + (y + 7)2 = 4

25. Given a circle with the equation (x + 5)2 + (y – 9)2 = 15, which of the following represents the center and radius of the circle?

A) center (−5, 9); radius = 15

B) center (5, −9); radius = 15

C) center (−5, 9); radius = 15

D) center (5, −9); radius = 15

26. Which is the equation of the circle on the graph?

A) (x + 1)2 + (y – 1)2 = 2

B) (x – 1)2 + (y + 1)2 = 4

C) (x + 1)2 + (y – 1)2 = 4

D) (x – 1)2 + (y + 1)2 = 2

27. Which of the following is the equation of the circle shown below?

A) (x – 3)2 + (y + 2)2 = 3

B) (x + 3)2 + (y – 2)2 = 3

C) (x – 3)2 + (y + 2)2 = 9

D) (x + 3)2 + (y – 2)2 = 9

28. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed from this

intersection?

A) square

B) triangle

C) parabola

D) straight line

29. Gina made a gelatin dessert in a cylindrical mold. She took it out of the mold, placed it

on a plate, and sliced it down the middle, as shown below.

What shape did Gina expose on each piece of the dessert where her cross-sectional cut

was made?

A) circle

B) oval

C) rectangle

D) trapezoid

30. Jason has a cube-shaped piece of cheese that measures 3 inches on each side. He slices

the cheese in half diagonally as shown below.

What is the shape of this cross section?

A) quadrilateral, but not square or rectangle

B) rectangle, but not square

C) rhombus

D) triangle

31. Paul bought a piece of cheese that was in the shape of a cylinder, as shown below.

He unwrapped the cheese and cut a thin slice off of the end. What would be the shape

of the cheese slice?

A) circle

B) triangle

C) rectangle

D) square

32. Which of the following drawings BEST represents a cross section of a sphere?

A) B) C) D)

33. The figure is a hexagonal pyramid.

Which figure shows a cross section of the pyramid parallel to its base?

A) B) C) D)

34. The length of one side of the base of the square pyramid measures 60 feet. The height

of the pyramid is 120 feet as shown below.

What is the volume of the pyramid?

A) 144,000 cubic feet

B) 216,000 cubic feet

C) 432,000 cubic feet

D) 864,000 cubic feet

35. A right square pyramid has a base with a perimeter of 36 inches. The height of the

pyramid is 8 inches, as shown below.

What is the volume of the pyramid?

A) 96 cubic inches

B) 216 cubic inches

C) 288 cubic inches

D) 648 cubic inches

36. Tony uses paper cones like the one shown below to serve snow cones. The

circumference of the top of the cone is 11 inches, and the height is 4 inches.

Which measurement is closest to the volume of the cone?

A)5

126

cubic inches

B) 2

143

cubic inches

C) 22 cubic inches

D) 1

513

cubic inches

37. The figure below shows the dimensions of a cylindrical soup can, in centimeters (cm).

The manufacturer has decided to redesign the can. The new can will be 0.5 centimeter

taller and 0.5 centimeter wider. By how much will the volume of the can increase in

the redesign?

A) 6.125π cubic centimeters

B) 24.250π cubic centimeters

C) 35.625π cubic centimeters

D) 43.625π cubic centimeters

38. The Ocean Salt Company is investigating the option of changing their container from a cylinder shape to a right rectangular prism

with the length and width shown below. The cylindrical container has a height of 14 centimeters (cm) and a diameter of

8.5 centimeters.

If the company wants the new container to have the

same volume as the cylindrical container, how tall

does the new container need to be, to the nearest

hundredth centimeter?

A) 6.23 cm

B) 8.12 cm

C) 12.46 cm

D) 13.23 cm

39. A storage shed is shown in the drawing with dimensions given in feet (ft).

What is the volume of the storage shed?

A) 190 cubic feet

B) 210 cubic feet

C) 240 cubic feet

D) 360 cubic feet

40. A truck hauled 136 cubic feet of sand to a construction site. The sand is dumped into a cone-shaped pile 6 feet in height. What is

the approximate diameter of the pile of sand, in feet?

A) 4.7

B) 9.3

C) 45.3

D) 68.0

41. How much water will fit into this cup?

A) 50.3 in.2

B) 113.1 in.2

C) 226.2 in.2

D) 452.2 in.2

42. If the height of the cylinder below is 4.5 centimeters and the volume is 40.5π

cubic centimeters, what is the length of the diameter of the base?

A) 1.5 cm

B) 3 cm

C) 4.5 cm

D) 6 cm

43. What is the volume, in cubic yards, of a pyramid that has a height of 10 yards and a square base that measures 3 yards on each

side?

A) 15

B) 30

C) 60

D) 90

44. David has a playhouse in his backyard that is shaped like a square prism with a square pyramid for the roof. What is the volume of

his playhouse if the house is 3 ft x 3 ft x 5 ft high and the roof is 3 ft x 3 ft x 2 ft high?

A) 45 cubic ft

B) 51 cubic ft

C) 63 cubic ft

D) 90 cubic ft

45. Which formula can be used to determine the volume of this 3

dimensional figure?

A) 3 314

3V x x

B) V = 4x3

C) 3 316

3V x x

D) 31

3V x

46. If the volume of a sphere is 24π what is the radius?

A) 18

B) 32

C) 3 18

D) 3 32

47. Which expression represents the volume of the sphere in cubic inches?

A) π × 152

B) 3415

3

C) 3115

3

D) π × 153

48. James has a cylinder and a cone with the same base area and height. The cylinder has a

radius of 3 inches, a height of 5 inches, and its volume is 45π in.3

James used the cone to fill the cylinder with rice and found that it took 3 cones full of

rice to fill the cylinder. Which formula can be used to find the volume of the cone?

A)23V r h

B)2V r h

C)2V r

D) 21

3V r h

49. Anna had a solid wooden dowel with a length of 12 inches and a diameter of 1 inch,

as shown below.

She cut a two-inch portion out of the dowel as indicated. What was the volume, to the

nearest tenth of a cubic inch, of the portion of the dowel that Anna cut out?

A) 1.6 cubic inches

B) 3.1 cubic inches

C) 6.3 cubic inches

D) 12.6 cubic inches

50. If the circumference of a cylinder is known, which other information must be known to find the volume of the cylinder?

A) π

B) radius

C) height

D) diameter

51. The diagram below shows a square pyramid with a volume of 400 cubic feet.

What is h, the height of this pyramid, in feet?

A)1

13

B) 4

C) 10

D) 12

52. The volume of the given cylinder is 282.74 cubic units.

Which is closest to the radius, r, of the base in units? (Use π ≈ 3.14)

A) 1.69

B) 3.00

C) 6.00

D) 9.42

53. Which is closest to the volume of the cylinder below, in cubic meters? (Use π ≈ 3.14)

A) 62.8

B) 87.9

C) 125.6

D) 251.2

54. Which process is MOST likely to be used to estimate the total surface area of the solid

shown below?

A) compute the area of 8 octagons and 2 trapezoids

B) find the perimeter of the base and multiply it by the height of the figure

C) find the perimeters of both bases and add them together

D) compute the area of 2 octagons and 8 trapezoids

55. Art classes are making paperweights in the shape of a hemisphere with a diameter of 4 inches,

as shown below. Find the amount of clay needed to form this paperweight.

A) 16.76 in.3

B) 25.13 in.3

C) 33.5 in.3

D) 50.27 in.3

56. The packaging for child's blocks is in shown below. Find the approximate volume of space

available in the packaging.

A) 61.94 in.3

B) 648 in.3

C) 1114.87 in.3

D) 1402.96 in.3

57. Which measurement is closest to the area of decorative paper that would be needed to cover the inside of a regular pentagonal

frame with a perimeter of 60 in.?

A) 991.0 in.2

B) 495.5 in.2

C) 247.8 in.2

D) 49.5 in.2

58. What is the mathematical name for the figure below?

A) Rectangular Prism

B) Rectangular Pyramid

C) Triangular Pyramid

D) Triangular Prism

59. An oatmeal container is in the shape of a right cylinder. Find the surface area of the container, to the nearest tenth, if the diameter

of the base is 10 centimeters and the height of the container is 16 centimeters.

A) 329.9 square centimeters

B) 534.1 square centimeters

C) 659.7 square centimeters

D) 6944.9 square centimeters

60. About how many square inches of leather are needed to cover the surface of a basketball if the radius of the basketball is 7 inches?

A) 153.9 square inches

B) 615.8 square inches

C) 1436.8 square inches

D) 2463.0 square inches

61. The open soup can shown has a radius of 2.2 inches and a height of 6.5 inches. Find the

surface area of the outside of the can if the lid is removed.

A) 60.13 square inches

B) 75.34 square inches

C) 105.05 square inches

D) 120.26 square inches

62. Find the surface area.

A) 75.4 square centimeters

B) 103.7 square centimeters

C) 131.9 square centimeters

D) 150.8 square centimeters

63. The surface area of a cube is 294 square feet. Find the volume.

A) 51.4 ft3

B) 216 ft3

C) 343 ft3

D) 1782.3 ft3

64. Find the surface area.

A) 144 cm2

B) 196 cm2

C)2144 24 3 cm

D) 288 cm2