Area&VolumeAssessment Name_____________________________Writeyouranswersinthespaceprovided. Page21

72°

9 cm

20 in

40°

6 cm

_________ 1. Find the sum of the measures of the interior angles of a dodecagon. _________ 2. What is the measure of each interior angle in a regular octagon? _________ 3. Find the number of sides of a regular polygon with each interior angle equal to 144°.

_________ 4. The measure of each exterior angle of a regular octagon is ______. [A] 22 5. ° [B] 135° [C] 45° [D] 67 5. ° _________ 5. In a farmer’s hexagonal field, when interior angles are put in increasing order, each differs from the next by 10°. Find the measure of the smallest interior angle of the field to the nearest .1 degree. [A] 120.0 ° [B] 117.7 ° [C] 97.3 ° [D] 95.0 ° _________ 6. Find the area of an equilateral triangle with side 6. _________ 7. Find the area of an equilateral triangle with side 4.

[A] 8 [B] 4 3 [C] 6 3 [D] 12 _________ 8. The area of an equilateral triangle that has a side length of 4 is _____.

[A] 6 2+ 3 sq. units [B] 8 sq. units

[C] 12 sq. units [D] 4 3 sq. units

_________ 9. Two similar trapezoids have areas

642

cm and 36 2cm . Find the ratio of similarity.

_________ 10. The ratio of the side lengths of two regular hexagons is 4 to 9. If the area of the smaller hexagon is 16 square units, then the area of the larger hexagon is _____.

[A] 64

9 sq. units [B] 36 sq. units

[C] 81 sq. units [D] 256

81 sq. units

_________ 11. If a circle has a radius of 7 inches, what is the circumference rounded to the nearest whole number? Use . .! " 314

[A] 22 in. [B] 44 in. [C] 88 in. [D] 154 in. _________ 12. A circle has a circumference of 45 meters. Find its diameter. [A] 14.32m [B] 22.5m [C] 7.16m [D] 11.25m _________ 13. Find the length of a 40° arc in a circle with a radius of 4.

[A] 16

9

!

[B] 8! [C]

9

8

!

[D]

8

9

!

_________ 14. Find the area of the shaded region. Use !" 314. . _________ 15. In this figure, each circle has a radius of 5 inches. What is the area of the portion outside the circles but inside the square? Express your answer in terms of ! . [A] 400 100 – ! [B] 40 20 – ! [C] 40 125 – ! [D] 400 25 – ! _________ 16. Find the area of the shaded region. [A] 50 27

2. cm [B] 11310

2. cm

[C] 28 272

. cm [D] 12 572

. cm

Area&VolumeAssessment Name_____________________________Writeyouranswersinthespaceprovided. Page22

9 cm

12 cm

15 cm

26 cm

8 m

11.9 m

7 m

6 m11 m

_________ 17. Each circle is tangent to the other two. If the diameter of the large circle is 12, the area of the shaded region is _____. [A] 36! sq. units

[B] 24! sq. units

[C] 18! sq. units [D] 9! sq. units

_________ 18. Find the number of vertices, faces, and edges for the figure below. [A] 7 vertices, 7 faces, 12 edges [B] 6 vertices, 7 faces, 12 edges [C] 8 vertices, 8 faces, 13 edges [D] 12 vertices, 7 faces, 7 edges _________ 19. Use Euler’s Theorem to calculate how many edges a polyhedron has if it has 4 faces and 4 vertices. _________ 20. Find the surface area of the triangular prism. [A] 1827.0 cm 2

[B] 42,120 cm 2

[C] 522.0 cm 2

[D] 1044.0 cm 2

_________ 21. Find the surface area of the cylinder to the nearest square unit. Use ! " 314. . [A] 500 m 2

[B] 159 m 2

[C] 95 m 2

[D] 1000 m 2 _________ 22. Find the surface area of the lateral faces on the regular pyramid below. [A] 336 ft2 [B] 168 ft2

[C] 84 ft2 [D] 532 ft2

_________ 23. A regular pyramid has a base area of

6 3 in.2 , a base perimeter of 12 in., and a slant

height of 4 3 in. Its surface area is _____.

[A] 30 3 in.2

[B] 36 in.2

[C] 24 3 in.2

[D] 54 3 in.2

_________ 24. The surface area of the right cone below is _____. [A] 44 in.

2!

[B] 112! in.2

[C] 36! in.2

[D] 16 33 in.2!

_________ 25. Find the exact volume of a cone that has a height of 17 inches and a radius of 2 inches. [A] 76! in3 [B] 38! in3

[C] 68

3! in3 [D] 68! in3

_________ 26. An aquarium in a restaurant is a rectangular prism and measures 4.5 feet by 6 feet by 4 feet. What is the volume of the aquarium? [A] 14.5 cubic feet [B] 28.5 cubic feet [C] 96 cubic feet [D] 108 cubic feet _________ 27. Find the volume of the right triangular prism. [A] 32 m3

[B] 462 m3

[C] 53 m3

[D] 231 m3 _________ 28. The volume of the right prism below is _____. [A] 120 ft3

[B] 60 ft3

[C] 30 13 ft3

[D] 10 13 ft3

Area&VolumeAssessment Name_____________________________Writeyouranswersinthespaceprovided. Page23

4 m

3 m

_________ 29. The volume of the right circular cylinder below is about _____. [A] 1061.9 m3

[B] 326.7 m3

[C] 265.5 m3

[D] 1036.9 m3 _________ 30. The volume of the pyramid below is _____. [A] 126! ft3

[B] 126 ft3

[C] 195! ft3

[D] 378 ft3 _________ 31. Calculate the volume of a cone with height 6 feet and radius 4 feet. _________ 32. Calculate the volume of the cone. Use ! " 314. .

[A] 113.04 m3

[B] 9.42 m3

[C] 37.68 m3

[D] 12 m3 _________ 33. 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 ! " 314. and

round to the nearest tenth. [A] 333.5 cm

3

[B] 351.2 cm3

[C] 333.4 cm3

[D] 378.0 cm3

_________ 34. Find the surface area of a sphere that has a diameter of 8 centimeters. Express your answer in terms of ! . _________ 35. Find the surface area of a sphere that has a diameter of 8 cm. Express your answer in terms of ! .

[A] 256 ! cm2

[B] 256

3! cm3

[C] 64 ! cm2

[D] 16 ! cm2

_________ 36. Use the figure above.The surface area of the sphere is about _____. [A] 434.9 ft2 [B] 277.6 ft2

[C] 92.5 ft2 [D] 69.4 ft2 _________ 37. Find the volume of a sphere 16 ft in diameter. Use ! " 314. and round your answer to

the nearest tenth. [A] 2167.3 ft3 [B] 1205.8 ft3

[C] 2143.6 ft3 [D] 301.4 ft3 _________ 38. The inside of an ice cream cone is filled with ice cream and has radius 5 cm and

height 7 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 ! and round your answer to the nearest tenth. [A] 7065. cm

3

[B] 8112. cm3

[C] 4215. cm3

[D] 444 8. cm3

_________ 39. The top of the cylindrical container below has the shape of a hemisphere. The total volume of the container is _____. [A] 36 in.

3

[B] 27! in.3

[C] 36 in.3! [D] 18 in.

3! Sides: _________ P: _________ V: _________ 40. The areas of corresponding faces of two similar pentagonal prisms are 36 cm

2 and 16 cm .2 What

is the ratio of the corresponding side lengths? of the perimeters of the corresponding faces? of the volumes?

Area&VolumeAssessment Name_____________________________Writeyouranswersinthespaceprovided. Page24

Reference: [11.1.1.1] [1] 1800 ° Reference: [11.1.1.9] [2] 135° Reference: [11.1.1.11] [3] 10 Reference: [11.1.1.15] [4] [C] Reference: [11.1.2.17] [5] [D] Reference: [11.2.1.18]

[6] 9 3 sq. units Reference: [11.2.1.19] [7] [B] Reference: [11.2.1.21] [8] [D] Reference: [11.3.1.32] [9] 4 : 3 Reference: [11.3.1.35] [10] [C] Reference: [11.4.1.40] [11] [B] Reference: [11.4.1.41] [12] [A] Reference: [11.4.1.47] [13] [D] Reference: [11.5.1.63]

[14] 50872

. cm Reference: [11.5.2.65] [15] [A] Reference: [11.5.2.67] [16] [D] Reference: [11.5.2.71] [17] [C] Reference: [12.1.1.2] [18] [A] Reference: [12.1.2.12] [19] 6 Reference: [12.2.1.15] [20] [D] Reference: [12.2.2.21] [21] [D] Reference: [12.3.1.25] [22] [A] Reference: [12.3.1.28] [23] [A] Reference: [12.3.2.31] [24] [A] Reference: [12.4.2.38] [25] [C] Reference: [12.4.1.35] [26] [D] Reference: [12.4.2.42] [27] [D]

Reference: [12.4.2.47] [28] [B] Reference: [12.4.2.48] [29] [A] Reference: [12.5.1.52] [30] [B] Reference: [12.5.1.54] [31] 32! ft3 Reference: [12.5.1.56] [32] [C] Reference: [12.5.2.61] [33] [D] Reference: [12.6.1.63] [34] 64 ! cm2 Reference: [12.6.1.64] [35] [C] Reference: [12.6.1.68] [36] [B] Reference: [12.6.2.71] [37] [C] Reference: [12.6.2.72] [38] [D] Reference: [12.6.2.75] [39] [C] Reference: [12.7.1.78] [40] 3:2; 3:2; 27:8