Deck 3: Geometry

Question 1

Estimate the measure of the angle in degrees and state whether the angle is acute, obtuse, or right.

A) , right
B) , obtuse
C) , obtuse
D) , acute
E) , acute

Answer 1

, right

Question 2

Estimate the measure of the angle in degrees and state whether the angle is acute, obtuse, or right.

A) , acute
B) , obtuse
C) , right
D) , acute
E) , obtuse

Answer 2

, obtuse

Question 3

Given that , find the measures of angles a and b.

A) ,
B) ,
C) ,
D) ,
E) ,

Answer 3

,

Question 4

Find the supplement of a 57° angle.

A) 237°
B) 303°
C) 147°
D) 123°
E) 33°

Question 5

Given AB = 9 in and the length of BC is the length of AB, find the length of AC.

A) 36 in
B) 3 in
C) 12 in
D) 27 in
E) 18 in

Question 6

Given TU = 4 m and UV is 5 times the length of TU, find the length of TV.

A) 20 m
B) 25 m
C) 21 m
D) 24 m
E) 10 m

Question 7

Find the complement of a 59° angle.

A) 121°
B) 21°
C) 31°
D) 149°
E) 239°

Question 8

Find the measure of .

A) 126°
B) 116°
C) 31°
D) 301°
E) 121°

Question 9

Estimate the measure of the angle in degrees and state whether the angle is acute, obtuse, or right.

A) , obtuse
B) , acute
C) , acute
D) , right
E) , obtuse

Question 10

Given that , find the measure of .

A) 141°
B) 39°
C) 129°
D) 151°
E) 133°

Question 11

Find the measure of .

A) 69°
B) 66°
C) 19°
D) 208°
E) 61°

Question 12

Find the measure of .

A) 286°
B) 16°
C) 96°
D) 106°
E) 254°

Question 13

Given AB = 8 mm, BC = 4 mm, and AD = 39 mm, find CD.

A) 27 mm
B) 31 mm
C) 35 mm
D) 51 mm
E) 28 mm

Question 14

Given = 47° and = 129°, find the measure of .

A) 176°
B) 133°
C) 137°
D) 75°
E) 82°

Question 15

Given is a right angle, find the measurement of .

A) 70°
B) 55°
C) 110°
D) 35°
E) 45°

Question 16

Find x.

A) 40°
B) 23°
C) 20°
D) 18°
E) 9°

Question 17

Given that , find the measures of angles a and b.

A) ,
B) ,
C) ,
D) ,
E) ,

Question 18

Find x.

A) 15°
B) 10°
C) 30°
D) 12°
E) 8°

Question 19

Find the measure of .

A) 86°
B) 108°
C) 342°
D) 187°
E) 118°

Question 20

Find x.

A) 13°
B) 14°
C) 11°
D) 8°
E) 29°

Question 21

Given that , find x.

A) x = 36°
B) x = 20°
C) x = 10°
D) x = 12°
E) x = 7°

Question 22

Given that , find the measures of and .

A) ;
B) ;
C) ;
D) ;
E) ;

Question 23

Find the perimeter of the figure.

A) 8.4 ft
B) 16.8 ft
C) 12.6 ft
D) 21.8 ft
E) 13.8 ft

Question 24

Wall-to-wall carpeting is installed in a room that is 16 ft long and 10 ft wide. The edges of the carpet are nailed to the floor. Along how many feet must the carpet be nailed down?

A) 26 ft
B) 36 ft
C) 52 ft
D) 42 ft
E) 160 ft

Question 25

Classify the triangle as acute, obtuse, or right.

A) acute
B) obtuse
C) right

Question 26

The radius of a circle measures 4.4 in. Find the circumference of the circle to the nearest hundredth.

A) 55.29 in
B) 29.65 in
C) 60.82 in
D) 13.82 in
E) 27.65 in

Question 27

Each of two sides of a triangular banner measures 22 cm. If the perimeter of the banner is 54 cm, what is the length of the third side of the banner?

A) 32 cm
B) 10 cm
C) 11 cm
D) 7 cm
E) 22 cm

Question 28

Given that and , find the measures of and .

A) ;
B) ;
C) ;
D) ;
E) ;

Question 29

Find the perimeter of the triangle.

A) 25 in
B) 31 in
C) 36 in
D) 46 in
E) 43 in

Question 30

Two angles of a triangle are 23° and 86°. Find the measure of the third angle.

A) 157°
B) 94°
C) 243°
D) 71°
E) 117°

Question 31

The length of each side of a square measures 7.5 in. Find the perimeter of the square.

A) 22.5 in
B) 30.0 in
C) 45.0 in
D) 37.5 in
E) 28.0 in

Question 32

Find the perimeter of a regular pentagon that measures 6.2 cm on each side.

A) 18.6 cm
B) 24.8 cm
C) 37.2 cm
D) 31.0 cm
E) 33.0 cm

Question 33

Classify the triangle as equilateral, isosceles, or scalene.

A) equilateral
B) scalene
C) isosceles

Question 34

The length of each of two sides of an isosceles triangle is cm. The third side measures cm. Find the perimeter of the triangle.

A) cm
B) cm
C) cm
D) cm
E) cm

Question 35

A bicycle wheel has a diameter of 24 inches. How many feet does the bicycle travel when the wheel makes 4 revolutions? Round your answer to the nearest hundredth.

A) 25.13 ft
B) 12.57 ft
C) 301.59 ft
D) 22.14 ft
E) 6.28 ft

Question 36

Find the circumference of the circle. Give the exact answer and the answer to the nearest hundredth.

A) m; 37.70 m
B) m; 75.40 m
C) m; 150.80 m
D) m; 452.39 m
E) m; 904.78 m

Question 37

One angle in a triangle is a right angle and one angle is 33°. What is the measure of the third angle?

A) 57°
B) 147°
C) 33°
D) 67°
E) 47°

Question 38

Name the polygon.

A) heptagon
B) pentagon
C) hexagon
D) quadrilateral

Question 39

Find the length of molding needed to put around a circular table 6.2 ft in diameter. Round your answer to the nearest hundredth.

A) 38.96 ft
B) 9.74 ft
C) 120.76 ft
D) 19.48 ft
E) 30.19 ft

Question 40

A rectangle has a length of 8.7 in and a width of 3.5 in. Find the perimeter of the rectangle.

A) 24.4 in
B) 12.2 in
C) 15.7 in
D) 20.9 in
E) 29.6 in

Question 41

A circle has a radius of 9 in. Find the increase in area when the radius is increased by 3 in. Round to the nearest hundredth.

A) 113.10 in²
B) 226.19 in²
C) 452.39 in²
D) 197.92 in²
E) 424.12 in²

Question 42

Find the area of the circle. Give both the exact value and an approximation to the nearest hundredth.

A) ;
B) ;
C) ;
D) ;
E) ;

Question 43

You are painting two walls of a store, one measuring 80 ft by 10 ft and the other measuring 60 ft by 10 ft. The paint costs $17.50 per gallon, and each gallon of paint will cover 200 ft². What is the cost to paint the two walls?

A) $59.50
B) $122.50
C) $152.50
D) $92.50
E) $420.00

Question 44

Find the area of the circle. Give both the exact value and an approximation to the nearest hundredth.

A) ;
B) ;
C) ;
D) ;
E) ;

Question 45

The radius of a circle is 9 cm. Find the area of the circle. Give the exact value.

A) 162 $\pi$ cm²
B) 9 $\pi$ cm²
C) 18F $\pi$ cm²
D) 324 $\pi$ cm²
E) 81 $\pi$ cm²

Question 46

A rectangular solid has a length of 12 cm, a width of 4.4 cm, and a height of 3.6 cm. Find the volume of the solid.

A) 20.00 cm³
B) 223.68 cm³
C) 191.68 cm³
D) 190.08 cm³
E) 380.16 cm³

Question 47

The lens on a telescope has a diameter of 200 in. Find the area of the lens of the telescope. Give the exact value.

A) 200 $\pi$ in ²
B) 10,000 $\pi$ in ²
C) 80,000 $\pi$ in ²
D) 160,000 $\pi$ in ²
E) 400 $\pi$ in ²

Question 48

Artificial turf is being used to cover a playing field. If the field is rectangular with a length of 150 yd and a width of 145 yd, how much artificial turf must be purchased to cover the field?

A) 43,500 yd²
B) 10,875 yd²
C) 590 yd²
D) 21,750 yd²
E) 295 yd²

Question 49

Find the volume of a cube whose side measures 5.8 cm.

A) 195.112 cm³
B) 33.640 cm³
C) 201.840 cm³
D) 1,170.672 cm³
E) 192.712 cm³

Question 50

The length of the base of a parallelogram is 24 cm, and the height is 8 cm. Find the area of the parallelogram.

A)
B)
C)
D)
E)

Question 51

A walkway 4 m wide surrounds a rectangular plot of grass. The plot is 28 m long and 20 m wide. What is the area of the walkway?

A) 208 m²
B) 1,008 m²
C) 384 m²
D) 478 m²
E) 448 m²

Question 52

Find the volume of the solid figure.

A) 504 in.³
B) 720 in.³
C) 360 in.³
D) 784 in.³
E) 740 in.³

Question 53

You plan to stain a wooden deck that measures 16 ft by 18 ft. A quart of stain will cover 70 ft². How many quarts of stain should you buy?

A) 4 qt
B) 7 qt
C) 5 qt
D) 2 qt
E) 9 qt

Question 54

Find the area of the figure.

A)
B)
C)
D)
E)

Question 55

The length of one base of a trapezoid is 18 cm, and the length of the other base is 16 cm. If the height is 11 cm, what is the area of the trapezoid?

A) 374 cm
B) 187 cm
C) 1584 cm
D) 45 cm
E) 748 cm

Question 56

Find the area of a square flower garden that measures 19 ft on each side.

A) 361 ft²
B) 722 ft²
C) 76 ft²
D) 1444 ft²
E) 38 ft²

Question 57

Find the area of the figure.

A)
B)
C)
D)
E)

Question 58

Find the volume of the sphere. Give both the exact value and an approximation to the nearest hundredth.

A) 0.6 $\pi$ cm³; 1.77 cm³
B) 3.4 $\pi$ cm³; 10.60 cm³
C) 4.5 $\pi$ cm³; 14.14 cm³
D) 9.0 $\pi$ cm³; 28.27 cm³
E) 13.5 cm³; 42.41 cm³

Question 59

The length of the base of a triangle is 3.5 km. The height is 3.7 km. Find the area of the triangle.

A) 12.95 km²
B) 25.90 km²
C) 6.48 km²
D) 45.33 km²
E) 6.80 km²

Question 60

The height of a triangle is 7 in. The area of the triangle is 63 in^2.. Find the length of the base of the triangle.

A) 9 in
B) 18 in
C) 36 in
D) 63 in
E) 126 in

Question 61

A hot air balloon is in the shape of a sphere. Approximately how much fabric was used to construct the balloon if its diameter is 29 ft? Round to the nearest whole number.

A) 10,568 ft²
B) 102,160 ft²
C) 2642 ft²
D) 661 ft²
E) 5284 ft²

Question 62

The height of a cone is 19 ft. The diameter of the cone is 20 ft. Find the volume of the cone. Round to the nearest hundredth.

A) 7958.70 ft³
B) 1989.68 ft³
C) 5969.03 ft³
D) 23876.10 ft³
E) 3780.38 ft³

Question 63

A rectangular solid has a square base and a height of 7 in. If the volume of the solid is 252 in³, find the length and width.

A) 3 in
B) 36 in
C) 6 in
D) 8 in
E) 42 in

Question 64

The slant height of a cone is 5.2 ft. The radius of the base is 3.7 ft. Find the surface area of the cone. Give the exact value.

A)
B)
C)
D)
E)

Question 65

The diameter of the base of a cylinder is 26 ft. The height of the cylinder is 24 ft. Find the volume of the cylinder. Round to the nearest hundredth.

A) 50,969.20 ft³
B) 4056.00 ft³
C) 23,524.25 ft³
D) 12,742.30 ft³
E) 980.18 ft³

Question 66

The surface area of a rectangular solid is 108 m². The height of the solid is 3 m, and the length is 6 m. Find the width of the rectangular solid.

A) 4 m
B) 8 m
C) 9 m
D) 6 m
E) 7 m

Question 67

Find the surface area of the cylinder. Give both the exact value and an approximation to the nearest hundredth.

A) ; 263.89 in²
B) ; 301.59 in²
C) ; 188.50 in²
D) ; 226.19 in²
E) ; 75.40 in²

Question 68

The volume of a cylinder with a height of 8 ft is 480 ft³. Find the radius of the base of the cylinder. Round to the nearest hundredth.

A) 4.37 ft
B) 19.10 ft
C) 13.73 ft
D) 5.85 ft
E) 3.60 ft

Question 69

The diameter of the base of a cylinder is 7.2 ft. The height of the cylinder is 3.7 ft. Find the surface area of the cylinder. Give the exact value.

A) 52.56 $\pi$ ft²
B) 39.60 $\pi$ ft²
C) 25.92 $\pi$ ft²
D) 26.64 $\pi$ ft²
E) 47.95 $\pi$ ft²

Question 70

The height of a pyramid is 19 in. The length of the side of the base is 20 in. Find the volume of the pyramid. Round to the nearest hundredth.

A) 1989.68 in³
B) 2533.33 in³
C) 7600 in³
D) 633.33 in³
E) 2406.67 in³

Question 71

An oil storage tank, which is in the shape of a cylinder, is 12 m high and has a diameter of 22 m. The oil storage tank is two-fifths full. Find the number of cubic meters of oil in the tank. Round to the nearest hundredth.

A) 10,947.82 m³
B) 4561.59 m³
C) 2985.77 m³
D) 2736.96 m³
E) 4361.96 m³

Question 72

How much glass is needed to make a fish tank that is 24 in. long, 22 in. wide and 8 in. high? The fish tank is open at the top.

A) 1792 in²
B) 1616 in²
C) 1600 in²
D) 4224 in²
E) 1264 in²

Question 73

The height of a rectangular solid is 12 cm. The length is 8 cm, and the width is 6 cm. Find the surface area of the solid.

A) 216 cm²
B) 576 cm²
C) 432 cm²
D) 336 cm²
E) 1,152 cm²

Question 74

The diameter of a sphere is 10 cm. Find the volume of the sphere. Give the exact measure.

A) cm³
B) cm³
C) cm³
D) cm³
E) cm³

Question 75

Find the surface area of the figure.

A) 81 m²
B) 36 m²
C) 72 m²
D) 27 m²
E) 45 m²

Question 76

The length of a side of the base of a pyramid is 3 cm, and the slant height is 7 cm. How much larger is the surface area of this pyramid than the surface area of a cone with a diameter of 3 cm and a slant height of 7 cm? Round to the nearest hundredth.

A) 52.94 cm²
B) 10.94 cm²
C) 22.04 cm²
D) 19.94 cm²
E) 12.38 cm²

Question 77

Find the surface area of the figure.

A) 31 m²
B) 30 m²
C) 16 m²
D) 10 m²
E) 62 m²

Question 78

The length of a side of the base of a pyramid is 7 m, and the slant height is 10 m. Find the surface area of the pyramid.

A) 329 m²
B) 189 m²
C) 140 m²
D) 119 m²
E) 238 m²

Question 79

The side of a cube measures 2.8 in. Find the surface area of the cube. Round your answer to three decimal places.

A) 21.952 in²
B) 7.840 in²
C) 131.712 in²
D) 47.040 in²
E) 23.520 in²