41. A cone is cut by a plane parallel to its base. The small cone on top is similar to the large cone. The ratio of the slant heights of the cones is 1 : 2. Find each ratio.

    

    1. the surface area of the large cone to the surface area of the small cone
    2. the volume of the large cone to the volume of the small cone
    3. the surface area of the frustum to the surface area of the large cone and to the surface area of the small cone
    4. the volume of the frustum to the volume of the large cone and to the volume of the small cone

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

42. The slant heights of two similar pyramids are in the ratio 1 : 5. The volume of the smaller pyramid is 60  m 3 . 60 , m cubed , .  What is the volume in cubic meters of the larger pyramid?

43. What is the value of x in the figure below?

    

44. A dilation maps Δ J E N cap delta j e n  onto Δ J ' E ' N ' . cap delta j , apostrophe e apostrophe n apostrophe .  If J E = 4.5  ft  , j e . equals 4.5 , ft , comma   E N = 6  ft  , e n , equals 6 , ft , comma  and J ' E ' = 13.5  ft  , j apostrophe e apostrophe . equals , 13.5 , ft , comma  what is E'N' in feet?

45. Δ C A R ≅ Δ B U S , m ∠ C = 25 , cap delta c eh r approximately equal to cap delta b u s comma m angle , c equals 25 , comma  and m ∠ R = 39 . m angle . r equals 39 .  What is m ∠ U ? m angle u question mark
46. A regular pentagon has a radius of 5 in. What is the area of the pentagon to the nearest square inch?

Mixed Review

See Lesson 11-6.

47. Sports Equipment The circumference of a regulation basketball is between 75 cm and 78 cm. What are the smallest and the largest surface areas that a basketball can have? Give your answers to the nearest whole unit.

Find the volume of each sphere to the nearest tenth.

48. diameter = 6  in  . diameter , equals 6 . in , .
49. circumference = 2 . 5 π  m circumference . equals 2 . . 5 pi m
50. radius = 6  in  . radius , equals 6 . in , .

See Lesson 7-4.

51. The altitude to the hypotenuse of right Δ A B C cap delta eh b c  divides the hypotenuse into 12-mm and 16-mm segments. Find the length of each of the following.
    1. the altitude to the hypotenuse
    2. the shorter leg of Δ A B C cap delta eh b c
    3. the longer leg of Δ A B C cap delta eh b c

Get Ready! To prepare for Lesson 12-1, do Exercises 52–54.

See Lesson 8-1.

Find the value of x.

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