41. A sector has been cut out of the disk below. The radii of the part that remains are taped together, without overlapping, to form the cone. The cone has a lateral area of 64 π   cm 2 . 64 pi , cm squared , . Find the measure of the central angle of the cutout sector.

    

Each given figure fits inside a 10-cm cube. The figure's base is in one face of the cube and is as large as possible. The figure's vertex is in the opposite face of the cube. Draw a sketch and find the lateral and surface areas of the figure.

42. a square pyramid
43. a cone

Standardized Test Prep

SAT/ACT

44. To the nearest whole number, what is the surface area of a cone with diameter 27 m and slant height 19 m?
    1. 1378   m 2 1378 , , m squared
    2. 1951   m 2 1951 , , m squared
    3. 2757   m 2 2757 , , m squared
    4. 3902   m 2 3902 , , m squared
45. What is the hypotenuse of a right isosceles triangle with leg 2 6 ? 2 square root of 6 question mark
    6. 4 6 4 square root of 6
    7. 2 3 2 square root of 3
    8. 4 3 4 square root of 3
    9. 4 2 4 square root of 2
46. Two angles in a triangle have measures 54 and 61. What is the measure of the smallest exterior angle?
    1. 119
    2. 115
    3. 112
    4. 126

Short Response

47. A diagonal divides a parallelogram into two isosceles triangles. Can the parallelogram be a rhombus? Explain.

Extended Response

48. ABCD has vertices at A(3, 4), B(7, 5), C(6, 1), and D( − 2 , − 4 negative 2 comma negative 4 ). A dilation with center (0, 0) maps A to A ′ ( 15 2 , 10 ) . eh prime . open . 15 over 2 , comma 10 . close . . What are the coordinates of B ′ , C ′ , b prime comma c prime comma and D ′ ? d prime question mark Show your work.

Mixed Review

See Lesson 11-2.

49. How much cardboard do you need to make a closed box 4 ft by 5 ft by 2 ft?
50. How much posterboard do you need to make a cylinder, open at each end, with height 9 in. and diameter 4 1 2 4 , and 1 half in.? Round your answer to the nearest square inch.

See Lesson 10-2.

51. A kite with area 195  in . 2 195 , in , . squared has a 15-in. diagonal. How long is the other diagonal?

Get Ready! To prepare for Lesson 11-4, do Exercises 52 and 53.

See Lessons 1-8 and 10-7.

Find the area of each figure. If necessary, round to the nearest tenth.

52. a square with side length 2 cm
53. a circle with diameter 15 in.

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