Deck 12: Geometry

Question 1

How many gallons of water can be stored in the spherical portion of the water tank shown in the illustration? (7.48 gal = 1 ft ³) Round your answer to the nearest thousand.

A) 328,000 gallons
B) 583,000 gallons
C) 582,000 gallons
D) 573,000 gallons
E) 590,000 gallons

Answer 1

583,000 gallons

Question 2

Follow the rules for working with measurements. Find the surface area and the volume of the sphere.

A) A = 8,230 m ², V = 99,400 m ³
B) A = 4,200 in. ², V = 24,900 in. ³
C) A = 4,120 in. ², V = 24,800 in. ³
D) A = 4,130 in. ², V = 24,810 in. ³
E) A = 4,090 in. ², V = 24,770 in. ³

Answer 2

A = 4,120 in. ², V = 24,800 in. ³

Question 3

A cooling water tower is in need of a larger ball float to shut off the inlet water when the tank is full. The present float is 6-inches in diameter and exerts 16-pounds of force. Calculations show that a ball having twice the volume would provide the necessary force. What is the diameter of the new float? Round your answer to the nearest hundredth.

A) 7.56 in.
B) 20.2 in.
C) 8.49 in.
D) 6 in.
E) 12 in.

Answer 3

7.56 in.

Question 4

A small ball bearing has a diameter of $0.615$ in. What is the volume of the bearing?

A) 0.109 in. ³
B) 0.238 in. ³
C) 0.088 in. ³
D) 0.122 in. ³
E) 0.0685 in. ³

Question 5

An experimental balloon is to have a diameter of 5.68 m. How much material is needed for this balloon?

A) 143 m ²
B) 23 m ²
C) 101 m ²
D) 25.3 m ²
E) 71.4 m ²

Question 6

Follow the rules for working with measurements. Find the surface area and the volume of the sphere.

A) A = 2,880 m ², V = 20,500 m ³
B) A = 1,370 ft ², V = 5,190 ft ³
C) A = 1,430 ft ², V = 5,140 ft ³
D) A = 1,470 ft ², V = 5,100 ft ³
E) A = 1,440 ft ², V = 5,130 ft ³

Question 7

A balloon 30.2 m in radius is to be filled with helium. How many m ³ of helium are needed to fill it?

A) 64,700 m ³
B) 126,000 m ³
C) 107,000 m ³
D) 119,000 m ³
E) 115,000 m ³

Question 8

A spherical tank for liquefied petroleum is 16 in. in diameter. What is the ratio of surface area to the volume of the tank?

A) $\frac { \pi } { 8 }$
B) $\frac { 8 } { 3 }$
C) $\frac { 2 } { 1 }$
D) $\frac { 3 } { 8 \pi }$
E) $\frac { 3 } { 8 }$

Question 9

You are designing a dome house in the shape of a hemisphere with a 31 ft outside diameter. Two coats of sealer are required to cover and seal the exposed external concrete. If one gallon covers 110 ft ², how many gallons are required for the bill of materials?

A) 27 gallons
B) 54 gallons
C) 20 gallons
D) 30 gallons
E) 40 gallons

Question 10

A welder has a large pan that has the shape of a hemisphere that is used for scrap metal pieces. If the radius of this pan is 7.00 in., what is the volume?

A) 404 in. ³
B) 720 in. ³
C) 1,440 in. ³
D) 1,550 in. ³
E) 680 in. ³

Question 11

Follow the rules for working with measurements.
An experimental balloon is to have a diameter of 5.73 m. How much material is needed for this balloon?
A = __________ m²

Question 12

A canister of coolant used to charge an air conditioner is cylindrical with a hemispherical top. What is the volume of the canister if the canister is 1.3 ft tall with a radius of 4 in.?

A) 1,050 in. ³
B) 1,040 in. ³
C) 1,480 in. ³
D) 918 in. ³
E) 554 in. ³

Question 13

You are designing a dome house in the shape of a hemisphere with a 37 ft outside diameter. If the walls are 12 in. in thick, what is the weight of this house? Concrete weighs 148 lb/ft ³. Assume doors and windows cover 15% of the house.

A) 257,000 lb
B) 254,000 lb
C) 256,000 lb
D) 259,000 lb
E) 541,000 lb

Question 14

Find the volume of the cylindrical shaped silo with a hemispherical top shown in the illustration.

A) 426,000 ft ³
B) 495,000 ft ³
C) 437,000 ft ³
D) 438,000 ft ³
E) 444,000 ft ³

Question 15

Follow the rules for working with measurements. Find the surface area and the volume of the sphere.

A) A = 606 m ², V = 1,450 m ³
B) A = 561 m ², V = 1,495 m ³
C) A = 176 m ², V = 264 m ³
D) A = 646 m ², V = 1,410 m ³
E) A = 616 m ², V = 1,440 m ³

Question 16

You are designing a dome house in the shape of a hemisphere with a 35 ft outside diameter. How many square feet of "stucco" should be listed on the bill of materials as needed to cover this home if 15% of it is windows and doors?

A) 1,640 ft ²
B) 1,620 ft ²
C) 1,670 ft ²
D) 1,650 ft ²
E) 3,270 ft ²

Question 17

Follow the rules for working with measurements. A city drains 150,000 gal of water from a full spherical tank with a radius of 29 ft. How many gallons of water are left in the tank? (7.48 gal = 1 ft ³)

A) 600,000 gallons
B) 620,000 gallons
C) 660,000 gallons
D) 640,000 gallons
E) 610,000 gallons

Question 18

Follow the rules for working with measurements. Find the surface area and the volume of the sphere.

A) A = 4,250 cm ², V = 26,100 cm ³
B) A = 4,240 cm ², V = 26,090 cm ³
C) A = 462 m ², V = 12,800 m ³
D) A = 4,280 cm ², V = 26,130 cm ³
E) A = 4,175 cm ², V = 26,045 cm ³

Question 19

An experimental aircraft has a plexiglass covering over the cockpit that is hemispherical. If the radius of the hemisphere is 2.00 ft, what is the surface area?

A) 17.3 ft ²
B) 35.3 ft ²
C) 40.4 ft ²
D) 25.1 ft ²
E) 50.3 ft ²

Question 20

You are designing a dome house in the shape of a hemisphere with a 38 ft outside diameter. Find the volume, which is needed to calculate the heat pump size.

A) 21,500 ft ³
B) 14,600 ft ³
C) 14,300 ft ³
D) 14,400 ft ³
E) 14,100 ft ³

Question 21

Find the circumference and the area of the circle. Use the rules for working with measurements.

A) The circumference is 313 mi, the area is 15,600 mi ².
B) The circumference is 626 mi, the area is 15,600 mi ².
C) The circumference is 313 mi, the area is 7,790 mi ².
D) The circumference is 157 mi, the area is 15,600 mi ².
E) The circumference is 626 mi, the area is 11,690 mi ².

Question 22

A round metal duct has a cross-section area of 134 square inches. What is the duct's diameter? Use the rules for working with measurements.

A) The diameter is 10.3 in.
B) The diameter is 13.1 in.
C) The diameter is 26.1 in.
D) The diameter is 6.53 in.
E) The diameter is 52.2 in.

Question 23

In the illustration, $\overline { A B }$ and $\overline { A C }$ are secants; $\overline { C D}$ and $\overline { B F }$ are chords. Suppose ?DCF = $35$ °, ?EFC = $42$ ° , and $\widehat{ C F }$ arc degrees. Find $\widehat { B D }$ in arc degrees.

A) $\widehat { B D }$ = $140$ °
B) $\widehat { B D }$ = $100$ °
C) $\widehat { B D }$ = $70$ °
D) $\widehat { B D }$ = $115$ °
E) $\widehat { B D }$ = $110$ °

Question 24

A boiler 4 ft in diameter is to be placed in a corner of a room shown in Illustration. How far from corner C are points A and B of the boiler? How long is a pipe from C to the center of the boiler M ? Round your answer to the nearest hundredth.

A) CA = CB = 6 ft, CM = 3 ft.
B) CA = CB = 4 ft, CM = 4 ft.
C) CA = CB = 8 ft, CM = 8 ft.
D) CA = CB = 2 ft, CM = 2.83 ft.
E) CA = CB = 4 ft, CM = 8 ft.

Question 25

In the illustration, find the area of the rectangular piece of metal after the two circles are removed. Use the rules for working with measurements.

A) The area is 4,392 cm ².
B) The area is 549 cm ².
C) The area is 2,196 cm ².
D) The area is 1,410 cm ²
E) The area is 1,098 cm ².

Question 26

How many degrees are in a central angle whose arc is $\frac { 1 } { 6 }$ of a circle?

A) $4$ °
B) $240$ °
C) $270$ °
D) $60$ °
E) $90$ °

Question 27

The area of a circle is 215 ft ². Find its radius. Use the rules for working with measurements.

A) The radius is 11.7 ft.
B) The radius is 16.5 ft.
C) The radius is 4.14 ft.
D) The radius is 8.27 ft.
E) The radius is 23.4 ft.

Question 28

In the illustration, the length of AC is 2, and the distance between B and center C is 6. Find the length of $\overline{AB}$ . Round your answer to the nearest hundredth.

A) $\overline { A B } = 5.55$
B) $\overline { A B } = 8.49$
C) $\overline { A B } = 11.31$
D) $\overline { A B } = 5.66$
E) $\overline { A B } = 1.77$

Question 29

If the diameter of a wheel's rim is 23 in., what is the rim's circumference? Use the rules for working with measurements.

A) The length is 18.1 in.
B) The length is 36.1 in.
C) The length is 72.3 in.
D) The length is 415 in.
E) The length is 831 in.

Question 30

A pipe has a 4.05-in. outside diameter and a 3.8-in. inside diameter. (See the illustration.) Find the area of its cross section. Use the rules for working with measurements.

A) The area is 0.785 in ².
B) The area is 3.08 in ².
C) The area is 0.771 in ².
D) The area is 6.17 in ².
E) The area is 1.54 in ².

Question 31

Find the area and perimeter of the figure in the illustration. Use the rules for working with measurements.

A) The perimeter is 105 in., the area is 521 in ².
B) The perimeter is 82.3 in., the area is 370 in ².
C) The perimeter is 130 in., the area is 1,440 in ².
D) The perimeter is 162 in., the area is 1,042 in ².
E) The perimeter is 130 in., the area is 841 in ².

Question 32

A round plate $14$ in. in diameter is to have ten holes drilled through it. This is accomplished by creating a drawing for half the circle and the then "mirroring" the drawing for the other half of the circle. The $\frac { 1 } { 2 }$ in. diameter holes are to be equally spaced on a $10$ in. concentric circle in the top half of the plate. What is the angle A between the holes? What is the angle B between the horizontal and each of the end holes?

A) A = $36$ °, B = $30$ °
B) A = $72$ °, B = $36$ °
C) A = $60$ °, B = $30$ °
D) A = $60$ °, B = $18$ °
E) A = $36$ °, B = $18$ °

Question 33

The airspeed indicator of an airplane is circular, with a diameter of 2.75 in. Use the rules for working with measurements. What is the circumference and area of the indicator?

A) The length is 8.64 in., the area is 11.9 in ².
B) The length is 8.64 in., the area is 23.8 in ².
C) The length is 17.3 in., the area is 11.9 in ².
D) The length is 8.64 in., the area is 5.94 in ².
E) The length is 17.3 in., the area is 5.94 in ².

Question 34

Find the length of the diameter of a circular silo with circumference 64 ft. Use the rules for working with measurements.

A) The diameter is 30.6 ft.
B) The diameter is 40.7 ft.
C) The diameter is 81.5 ft.
D) The diameter is 20.4 ft.
E) The diameter is 201 ft.

Question 35

Find the circumference and the area of the circle. Follow the rules for working with measurements.

A) The circumference is 408 m, the area is 6,640 m ².
B) The circumference is 204 m, the area is 50 m ².
C) The circumference is 204 m, the area is 13,300 m ².
D) The circumference is 102 m, the area is 6,640 m ².
E) The circumference is 204 m, the area is 3,320 m ².

Question 36

Find the measure of the unknown angle.

A) x = 129.3°
B) x = 30.1°
C) x = 64.7°
D) x = 137.3°
E) x = 63.3°

Question 37

Find the measure of $$\angle 1$$ in the illustration.

A) ?1 = 90°
B) ?1 = 120°
C) ?1 = 30°
D) ?1 = 180°
E) ?1 = 60°

Question 38

The circumference of a circle is 70.7 m. Find its radius. Use the rules for working with measurements.

A) The radius is 4.74 m.
B) The radius is 11.3 m.
C) The radius is 5.63 m.
D) The radius is 22.5 m.
E) The radius is 45.0 m.

Question 39

A circular metal tank has a radius of 20 in. If a lid made for tank has the same radius, find the area of the lid in square feet. Use the rules for working with measurements.

A) The area is 34.9 ft ².
B) The area is 8.73 ft ².
C) The area is 1,260 ft ².
D) The area is 4.36 ft ².
E) The area is 17.5 ft ².

Question 40

Find the circumference and the area of the circle. Use the rules for working with measurements.

A) The circumference is 25.1 in, the area is 201 in ².
B) The circumference is 50.3 in, the area is 25.1 in ².
C) The circumference is 25.1 in, the area is 50.3 in ².
D) The circumference is 50.3 in, the area is 101 in ².
E) The circumference is 12.6 in, the area is 101 in ².

Question 41

In the illustration, $\overline { A B } \| \overline { C D }$ . Find the lengths of $\overline { AC }$ and $$\overline{C D}$$ .

A) AO is equal to 4
CD is equal to $3 \sqrt { 5 }$
B) AO is equal to 4.4
CD is equal to $4 \sqrt { 5 }$
C) AO is equal to 8.4
CD is equal to $2 \sqrt { 5 }$
D) AO is equal to 4.4
CD is equal to $2 \sqrt { 5 }$
E) AO is equal to 8.4
CD is equal to $3 \sqrt { 5 }$

Question 42

How many degrees are in a central angle whose arc is of a circle?
__________ °

Question 43

A machinist must follow a part drawing with scale 1 to 24. Find the dimensions of the finished stock shown in the illustration. That is, find lengths A, B, C, D.

A) A = 74 in., B = 11 in., C = 54 in., D = 5 in.
B) A = 10 in., B = 74 in., C = 52 in., D = 5 in.
C) A = 74 in., B = 10 in., C = 52 in., D = 4 in.
D) A = 4 in., B = 52 in., C = 10 in., D = 74 in.
E) A = 74 in., B = 10 in., C = 4 in., D = 52 in.

Question 44

A landing pad for a helicopter at a hospital has the shape of a regular hexagon. The perimeter of this landing pad is $28.8 \overline { 0 } 0$ ft with each side $48 \overline { 0 }$ ft. At another hospital has a similar landing pad with perimeter $29.4 \overline { 0 } 0$ ft. What is the length of each of its sides?

A) $49 \overline { 0 }$ ft
B) $43 \overline { 0 }$ ft
C) $59 \overline { 0 }$ ft
D) $47 \overline { 0 }$ ft
E) $50 \overline { 0 }$ ft

Question 45

The perimeter of a regular heptagonal shaped piece of flat steel is 42 in., six inches per side. If a welder is to cut another piece of flat steel that is similar but with a 77 in. perimeter, what is the length of each side?

A) 11 in.
B) 15 in.
C) 5 in.
D) 19 in.
E) 7.4 in.

Question 46

Find the length of DE in the illustration.

A) DE is 15.5 m
B) DE is 12.7 m
C) DE is 11.1 m
D) DE is 13.2 m
E) DE is 14.3 m

Question 47

In the illustration, suppose $$\overline { D E } \| \overline { B C }$$ . Find DE.

A) DE is equal to 5.
B) DE is equal to 7.
C) DE is equal to 4.
D) DE is equal to 3.
E) DE is equal to 12.

Question 48

A tree casts a shadow $$11\bar0$$ ft long when a vertical rod 4 ft high casts a shadow 2 ft long. (See Illustration.) How tall is the tree?

A) The tree is 260 ft long.
B) The tree is 220 ft long.
C) The tree is $22 \overline { 0 }$ ft long.
D) The tree is 250 ft long.
E) The tree is $26 \overline { 0 }$ ft long.

Question 49

Find the length of BC in the illustration.

A) BC is 27.4 m
B) BC is 29.4 m
C) BC is 29.9 m
D) BC is 27.9 m
E) BC is 30 m

Question 50

Use the rules for working with measurements.
The area of a circle is 157 . Find its radius.
r = __________ ft

Question 51

Use the rules for working with measurements. Find the circumference of the circle.
C = __________ in.
Find the area of the circle.
A = __________

Question 52

Use the rules for working with measurements. Find the circumference of the circle.
C = __________ m
Find the area of the circle.
A = __________

Question 53

In the illustration, polygon ABCD is similar to polygon FGHI. Find∠H, FI, IH, BC. Round your answer to the nearest tenth.

A) ∠H = 90°, FI = 2.5, IH = 1.1, BC = 2.
B) ∠H = 45°, FI = 2.5, IH = 1.1, BC = 2.
C) ∠H = 60°, FI = 2.5, IH = 2, BC = 1.1.
D) ∠H = 90°, FI = 1.1, IH = 2, BC = 5.
E) ∠H = 90°, FI = 2, IH = 1.1, BC = 5.

Question 54

An inclined ramp is to be built so that it reaches a height of 12 ft over a 18 ft run. (See the illustration.) Braces are placed every 6 ft. Find the height of braces x and y.

A) x is equal to 4 ft, y is equal to 8 ft.
B) x is equal to 11 ft, y is equal to 22 ft.
C) x is equal to 3 ft, y is equal to 22 ft.
D) x is equal to 3 ft, y is equal to 6 ft.
E) x is equal to 7 ft, y is equal to 14 ft.

Question 55

In Illustration and are secants; and are chords. Suppose ∠DFC = °, ∠EFC = °, and arc degrees. Find the number of arc degrees in . __________ °

Question 56

Use the rules for working with measurements.
Find the measure of the unknown angle.  
x =            °

Question 57

In the illustration, $\overline { A B } \| \overline { C D }$ . Is triangle ABO similar to triangle CDO? Why or why not?

A) No, OC is three times as long as BO is.
B) Yes, all angles of ABO are equal to corresponding angles of DCO.
C) Neither of the other explanations is correct.

Question 58

A right triangular support gusset is to be made similar to another right triangular gusset. The smaller gusset has sides with lengths 5 in. and 7.5 in. Find the length of the corresponding side of the larger triangle if its larger side has length 17.4 in.

A) 13.8 in.
B) 11.6 in.
C) 11.8 in.
D) 13.1 in.
E) 10.9 in.

Question 59

In the illustration, quadrilaterals ABCD and WXYZ are similar rectangles. AB = 20, BC = 12, and XY = 15. Find YZ.

A) YZ is equal to 7.
B) YZ is equal to 9.
C) YZ is equal to 7.5.
D) YZ is equal to 16.
E) YZ is equal to 10.

Question 60

Use the rules for working with measurements.
The circumference of a circle is 70.8 m. Find its radius.
r = __________ m

Question 61

Find x and y to three significant digits using the formula s = r? (? in radians).   $$\begin{array} { | c | c | c | } \hline \text { Radius, } r & \text { Angle, } \Theta & \text { Distance, } s \\\hline 12 \mathrm {~cm} & 55 ^ { \circ } & x \mathrm {~cm} \\\hline 16 \mathrm {~mm} & 70 ^ { \circ } & y \mathrm {~mm} \\\hline\end{array}$$

A) x = 3.667; y = 6.222
B) x = 11.519; y = 19.548
C) x = 36.189; y = 61.411
D) x = 115.192; y = 195.477
E) x = 36.189; y = 6.222

Question 62

A polygon cross-sectional duct is to be exposed and painted. It is to be attached to a same-shaped, but smaller duct. If the dimensions of the ducts are AB = 18 in., DE = 30 in., A'B' = 6 in., find D'E'?

A) 10 in.
B) 20 in.
C) 2 in.
D) 30 in.
E) 4 in.

Question 63

Choose the value below that correctly fills in the blank. Round the result to three significant digits. 30 ^o = _________ rad

A) 0.262
B) 0.654
C) 1.571
D) 0.524
E) 0.349

Question 64

A small heater has a rectangular filter that is $13 \text { in. } \times 24 \text { in. }$ Another larger heater requires a similar filter that has a 26 in. width. What is the height of this larger filter?

A) 49 in.
B) 48 in.
C) 27 in.
D) 26 in.
E) 24 in.

Question 65

A 9 ft by 8 ft bookcase is to be built. It has horizontal shelves every foot. A support is to be notched in the shelves diagonally from one corner to the opposite corner. At what point should each of the shelves be notched? That is, find lengths A, B, C, D and E in the illustration. How long is the diagonal crosspiece? Round your answer to the nearest hundredth.

A) A = 1.3 ft, B = 2.7 ft, C = 4 ft, D = 5.3 ft,E = 6.7 ft, the crosspiece is 12 ft.
B) A = 1.5 ft, B = 3 ft, C = 4.5 ft, D = 6 ft,E = 7.5 ft, the crosspiece is 12.04 ft.
C) A = 1.5 ft, B = 3 ft, C = 5.5 ft, D = 5 ft,E = 7.5 ft, the crosspiece is 12.04 ft.
D) A = 1.33 ft, B = 2.67 ft, C = 4 ft, D = 5.33 ft,E = 6.67 ft, the crosspiece is 12.04 ft.
E) A = 1.5 ft, B = 3 ft, C = 4.5 ft, D = 6 ft,E = 6.5 ft, the crosspiece is 12 ft.

Question 66

An older car has a fan belt assembly that is the shape of an isosceles triangle. The two equal sides are 12.0 in. each and the third side is 9.6 in. An older truck has a similar fan belt arrangement but the triangle has width 19.6 in. What is the length of the two congruent sides of this triangle?

A) 20.2 in.
B) 18.6 in.
C) 17.4 in.
D) 21.4 in.
E) 24.5 in.

Question 67

A rectangular runway is 7,600 ft x 76 ft. A similar rectangular runway is 5,200 ft long. What is the width of this runway?

A) 52 ft
B) 520,000 ft
C) 54 ft
D) 61 ft
E) 46 ft

Question 68

Change 140 ^o to radians, and round the result to three significant digits.

A) 4.887 rad
B) 2.443 rad
C) 8,020 rad
D) 2.843 rad
E) 1.222 rad

Question 69

Find x and y to three significant digits using the formula s = rΘ (Θradians).  

A) x = 106.667; y = 400
B) x = 40; y = 67.021
C) x = 33.51; y = 125.664
D) x = 67; y = 251.327
E) x = 10.7; y = 40

Question 70

Find x and y to three significant digits using the formula s = r? (? in radians).   $$\begin{array} { | c | c | c | } \hline \text { Radius, } r & \text { Angle, } \Theta & \text { Distance, } s \\\hline 20 \mathrm {~cm} & x \mathrm { rad } & 52 \mathrm {~cm} \\\hline 10 \mathrm {~mm} & y \mathrm { rad } & 18 \mathrm {~mm} \\\hline\end{array}$$

A) x = 8.168; y = 5.655
B) x = 5.2; y = 3.6
C) x = 2.6; y = 3.6
D) x = 2.6; y = 1.8
E) x = 5.2; y = 1.8

Question 71

Change $\frac { \pi } { 12 }$ rad to degrees.

A) 3.75 ^o
B) 30 ^o
C) 7.5 ^o
D) 15 ^o
E) 17 ^o

Question 72

What percent of $2$ rad is $\frac { \pi } { 12 }$ rad? Round the result to the nearest tenth.

A) 0.1 %
B) 25.1 %
C) 13.1 %
D) 4.2 %
E) 13.3 %

Question 73

Find x and y to the nearest tenth using the formula s = rΘ (Θ in radians).  
Radius, r
Angle, Θ
Distance, s
20 cm
X ^o
20)94 cm
0)021 m
Y ^o
0)0205 m

A) x = 120 ^o; y = 175.7 ^o
B) x = 60 ^o; y = 175.7 ^o
C) x = 188.5 ^o; y = 111.9 ^o
D) x = 60 ^o; y = 111.9 ^o
E) x = 60 ^o; y = 55.9 ^o

Question 74

Find the number of radians in a central angle whose arc is $\frac { 3 } { 7 }$ of a circle.

A) $\frac { 6 } { 7 }$ rad
B) $\frac { 6 } { 7 } \pi$ rad
C) $\frac { 7 } { 6 } \pi$ rad
D) $\frac { 3 } { 7 } \pi$ rad
E) $\frac { 2 } { 9 } \pi$ rad

Question 75

Change $\frac { \pi } { 3 }$ rad to degrees.

A) 120 ^o
B) 59 ^o
C) 60 ^o
D) 4.5 ^o
E) 30 ^o

Question 76

The side mirror of a small pickup truck is similar to that a larger full size pickup truck. If the smaller truck has a rectangular side mirror with a width of 13.3 in. and a height of 15.2 in., what is the height of the larger mirror if its width is 16.8 in.?

A) 19.2 in.
B) 21.3 in.
C) 19.5 in.
D) 16.7 in.
E) 16.8 in.

Question 77

A vertical tower 141 ft high is anchored to the ground by guy wires as shown in the illustration. How long is each guy wire? Round your answer to the nearest hundredth.

A) A = 170 ft, B = 130 ft, C = 92 ft, D = 73 ft, E = 110 ft, F = 150 ft.
B) A = 167.28 ft, B = 129.54 ft, C = 91.81 ft, D = 72.95 ft, E = 110.68 ft, F = 148.41 ft.
C) A = 167 ft, B = 130 ft, C = 92 ft, D = 73 ft, E = 111 ft, F = 148 ft.
D) A = 166 ft, B = 129 ft, C = 91 ft, D = 74 ft, E = 110 ft, F = 149 ft.
E) A = 170 ft, B = 128 ft, C = 92 ft, D = 73 ft, E = 108 ft, F = 150 ft.

Question 78

Find x and y to three significant digits using the formula $s = n \Theta$ ( $\Theta$ in radians).   $\begin{array} { | c | c | c | } \hline \text { Radius, } r & \text { Angle, } & \text { Distance, } s \\\hline x \mathrm {~cm} & 25 ^ { \circ } & 15 \mathrm {~cm} \\\hline y \mathrm {~m} & 315 ^ { \circ } & 107 \mathrm {~m} \\\hline\end{array}$

A) x = 13.751; y = 38.925
B) x = 34.377; y = 19.462
C) x = 34.377; y = 61.143
D) x = 108; y = 19.462
E) x = 34.377; y = 38.925

Question 79

How many radians are contained in a central angle which is $\frac { 2 } { 3 }$ of a circle?

A) $\frac { 4 } { 3 }$ rad
B) $\frac { 4 } { 3 } \pi$ rad
C) $\frac { 2 } { 3 } \pi$ rad
D) $\frac { 3 } { 4 } \pi$ rad
E) $5 \pi$ rad

Question 80

Choose the value below that correctly fills in the blank. Round the result to the nearest tenth. 2.7 rad = __________ ^o

A) 152.7
B) 309.4
C) 77.3
D) 154.7
E) 0.5