Area&VolumeAssessment Name_____________________________Writeyouranswersinthespaceprovided. Page11

40°

7 cm

36 in.

72°

4 cm

_________ 1. Find the sum of the measures of the interior angles of an octagon. _________ 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 168°.

_________ 4. The measure of each exterior angle of a regular octagon is ______.

[A] 45° [B] 22 5. ° [C] 67 5. ° [D] 135° _________ 5. In a farmer’s pentagonal 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] 108.0 ° [B] 110.3 ° [C] 85.7 ° [D] 88.0 ° _________ 6. Find the area of an equilateral triangle with side 4. _________ 7. Find the area of an equilateral triangle with side 4.

[A] 12 [B] 6 3 [C] 4 3 [D] 8 _________ 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] 4 3 sq. units [D] 12 sq. units

_________ 9. Two similar trapezoids have areas

632

cm and 28 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] 36 sq. units [B] 64

9 sq. units

[C] 81 sq. units [D] 256

81 sq. units

_________ 11. If a circle has a radius of 6 inches, what is the circumference rounded to the nearest whole number? Use . .! " 314

[A] 38 in. [B] 113 in. [C] 19 in. [D] 76 in. _________ 12. A circle has a circumference of 33 meters. Find its radius. [A] 16.5 m [B] 10.5 m [C] 8.25 m [D] 5.25 m _________ 13. Find the length of a 40° arc in a circle with a radius of 4.

[A] 16

9

!

[B] 9

8

!

[C] 8! [D]

8

9

!

_________ 14. Find the area of the shaded region. Use !" 314. . _________ 15. In this figure, each circle has a radius of 6 inches. What is the area of the portion outside the circles but inside the square? Express your answer in terms of ! . [A] 1296 324 – ! [B] 72 216 – ! [C] 72 36 – ! [D] 1296 36 – ! _________ 16. Find the area of the shaded region. [A] 10 05

2. cm [B] 12 57

2. cm

[C] 50 272

. cm [D] 40 212

. cm

Area&VolumeAssessment Name_____________________________Writeyouranswersinthespaceprovided. Page12

21 cm

22 cm

30.4 cm

53 cm

5 m

8.2 m

7 m

5 m10 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] 9! sq. units

[B] 36! sq. units

[C] 24! sq. units [D] 18! sq. units

_________ 18. Find the number of vertices, faces, and edges for the figure below. [A] 12 vertices, 7 faces, 7 edges [B] 7 vertices, 7 faces, 12 edges [C] 8 vertices, 8 faces, 13 edges [D] 6 vertices, 7 faces, 12 edges _________ 19. Use Euler’s Theorem to calculate how many edges a polyhedron has if it has 20 faces and 12 vertices. _________ 20. Find the surface area of the triangular prism. [A] 4352.2 cm 2

[B] 744,374.4 cm 2

[C] 2176.1 cm 2

[D] 3264.2 cm 2 _________ 21. Find the surface area of the cylinder to the nearest square unit. Use ! " 314. .

[A] 207 m 2

[B] 66 m 2

[C] 41 m 2

[D] 415 m 2 _________ 22. Find the surface area of the lateral faces on the regular pyramid below. [A] 336 ft2 [B] 532 ft2

[C] 84 ft2 [D] 168 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] 24 3 in.2

[B] 36 in.2

[C] 54 3 in.2

[D] 30 3 in.2

_________ 24. The surface area of the right cone below is _____.

[A] 112! in.2

[B] 16 33 in.2!

[C] 36! in.2

[D] 44 in.2!

_________ 25. Find the exact volume of a cylinder that has a height of 13 inches and a radius of 3 inches. [A] 96! in3 [B] 117! in3

[C] 39! in3 [D] 48! in3 _________ 26. An aquarium in a restaurant is a rectangular prism and measures 4.5 feet by 6 feet by 3 feet. What is the volume of the aquarium? [A] 22.5 cubic feet [B] 81 cubic feet [C] 72 cubic feet [D] 13.5 cubic feet _________ 27. Find the volume of the right triangular prism. [A] 350 m3

[B] 27.5 m3

[C] 175 m3

[D] 45 m3 _________ 28. The volume of the right prism below is _____. [A] 120 ft3 [B] 60 ft3 [C] 30 13 ft

3

[D] 10 13 ft3

Area&VolumeAssessment Name_____________________________Writeyouranswersinthespaceprovided. Page13

9 m

8 m

_________ 29. The volume of the right circular cylinder below is about _____. [A] 1036.9 m3

[B] 265.5 m3

[C] 1061.9 m3

[D] 326.7 m3 _________ 30. The volume of the pyramid below is _____. [A] 378 ft3 [B] 126 ft3

[C] 126! ft3 [D] 195! ft3 _________ 31. Calculate the volume of a cone with height 7 feet and radius 4 feet. _________ 32. Calculate the volume of the cone. Use ! " 314. .

[A] 66.99 m3

[B] 192 m3

[C] 1808.64 m3

[D] 602.88 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] 378.0 cm

3

[B] 351.2 cm3

[C] 351.3 cm3

[D] 333.4 cm3

_________ 34. Find the surface area of a sphere that has a diameter of 10 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] 16 ! cm2

[B] 256 ! cm2

[C] 64 ! cm2

[D] 256

3! cm3

_________ 36. Use the figure. The surface area of the sphere is about _____. [A] 277.6 ft2 [B] 92.5 ft2

[C] 69.4 ft2 [D] 434.9 ft2 _________ 37. Find the volume of a sphere 16 ft in diameter. Use ! " 314. and round your answer to

the nearest tenth. [A] 301.4 ft3 [B] 1205.8 ft3

[C] 2143.6 ft3 [D] 267.9 ft3 _________ 38. The inside of an ice cream cone is filled with ice cream and has radius 6 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] 7159. cm

3

[B] 11681. cm3

[C] 12434. cm3

[D] 692 6. cm3

_________ 39. The top of the cylindrical container below has the shape of a hemisphere. The total volume of the container is _____. [A] 18 in.

3! [B] 36 in.3!

[C] 36 in.3

[D] 27! in.3

Sides: _________ P: _________ V: _________ 40. The areas of corresponding faces of two similar hexagonal prisms are 25 cm

2 and 144 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. Page14

Reference: [11.1.1.1] [1] 1080 °

Reference: [11.1.1.9] [2] 135°

Reference: [11.1.1.11] [3] 30

Reference: [11.1.1.15] [4] [A]

Reference: [11.1.2.17] [5] [D]

Reference: [11.2.1.18]

[6] 4 3 sq. units

Reference: [11.2.1.19] [7] [C]

Reference: [11.2.1.21] [8] [C]

Reference: [11.3.1.32] [9] 3 : 2

Reference: [11.3.1.35] [10] [C]

Reference: [11.4.1.40] [11] [A]

Reference: [11.4.1.41] [12] [D]

Reference: [11.4.1.47] [13] [D]

Reference: [11.5.1.63] [14] 171

2. cm

Reference: [11.5.2.65] [15] [A]

Reference: [11.5.2.67] [16] [A]

Reference: [11.5.2.71] [17] [D]

Reference: [12.1.1.2] [18] [B]

Reference: [12.1.2.12] [19] 30

Reference: [12.2.1.15] [20] [A]

Reference: [12.2.2.21] [21] [D]

Reference: [12.3.1.25] [22] [A]

Reference: [12.3.1.28] [23] [D]

Reference: [12.3.2.31] [24] [D]

Reference: [12.4.2.38] [25] [B]

Reference: [12.4.1.35] [26] [B]

Reference: [12.4.2.42] [27] [C]

Reference: [12.4.2.47] [28] [B]

Reference: [12.4.2.48] [29] [C]

Reference: [12.5.1.52] [30] [B]

Reference: [12.5.1.54]

[31] 112

3! ft3

Reference: [12.5.1.56] [32] [D]

Reference: [12.5.2.61] [33] [A]

Reference: [12.6.1.63] [34] 100 ! cm2

Reference: [12.6.1.64] [35] [C]

Reference: [12.6.1.68] [36] [A]

Reference: [12.6.2.71] [37] [C]

Reference: [12.6.2.72] [38] [A]

Reference: [12.6.2.75] [39] [B]

Reference: [12.7.1.78] [40] 5:12; 5:12; 125:1728