Free Printable Volume of 3D Shapes and Triangle Angles

1.

Find x.

a)

28.9

b)

61.1

c)

64.2

d)

25.8

2.

Find x.

a)

12.8

b)

77.2

c)

12.5

d)

77.5

3.

Find x.

a)

8.5

b)

31.9

c)

8.8

d)

34.2

4.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree. Round your answer to the nearest foot.

(a)

5.

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is closest to the height of the lighthouse?

a)

25 feet

b)

45 feet

c)

110 feet

d)

135 feet

6.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. How many degrees should the tourist tilt his camera down to photograph the deer? Round your answer to the nearest degree.

(a)

7.

CUBS is a Rhombus.
Find BC

a)

61.6

b)

30.8

c)

27

d)

13.5

8.

Solve for the missing angle

a)

50.5 degrees

b)

12.7 degrees

c)

36.9 degrees

d)

72.2 degrees

9.

What is the area of the following sector? (approximate pi to 3.14)

a)

452.16

b)

120

c)

150.72

d)

1,356.48

10.

Ship A leaves port P and travels on a bearing of 200°. A second ship B leaves the same port P and travels on a bearing of 165°. After half an hour ship A has travelled 5.2 km and ship B has travelled 5.8 km. How far apart are the ships after half an hour? Give the answer to three significant figures.

a)

3.46 km

b)

4.26 km

c)

3.36 km

d)

4.56 km

11.

A car drives around a roundabout with a 80 ft radius. The roads it enters and exits from are 100° apart. How far around the roundabout does the car drive?

a)

120 ft

b)

140 ft

c)

160 ft

12.

What is the length of this arc, with an angle of 12° and a radius of 5 mm?

a)

1.05 mm

b)

1/3

c)

30 mm

13.

In the diagram with parallel chords, find the measure of the arc marked with an x.

a)

40

b)

80

c)

120

d)

240

14.

In the diagram, AB, BC and AC are tangents to circle O at points F, E, and D, respectively, AF = 6, CD = 5, and BE = 4.

What is the perimeter of $\Delta ABC$ ?

a)

15

b)

25

c)

60

d)

30

15.

In the diagram of circle O, PA is tangent to circle O at A, and PBC is a secant with points B and C on the circle.

If PA = 8 and PB = 4, what is the length of PC?

a)

16

b)

20

c)

15

d)

12

16.

Secants JKL and JMN are drawn to circle O from an external point, J. If JK = 8, LK = 4, and JM = 6, what is the length of JN?

(Diagram not drawn to scale.)

a)

16

b)

12

c)

10

d)

8

17.

In the diagram of circle O, chords AD and BC intersect at E, m arcAC = 87, and m arcBD = 35.

What is the degree measure of $\angle CEA$ ?

a)

87

b)

61

c)

43.5

d)

26

18.

In the diagram, AC and AD are tangent to circle B at points C and D, respectively, and BC, BD, and BA are drawn.

If AC = 12 and AB = 15, what is the length of BD?

a)

5.5

b)

9

c)

12

d)

18

19.

In circle O, diameter DB is perpendicular to chord AC at E. If DB = 34 and AC = 30, what is the length of OE?

a)

8

b)

9

c)

16

d)

25

20.

Given the circle in the diagram with center O. Find the measure of angle x.

a)

40

b)

80

c)

50

d)

100

21.

In the diagram of circle O, $m\angle OAB\ =\ 50^o$ . Find $m\ arcAB$ .

a)

100

b)

25

c)

80

d)

40

22.

In the diagram of two intersecting chords, find the degree measure of the arc marked with an x.

a)

120

b)

20

c)

30

d)

60

23.

If m<PQR=141, find the value of x.

a)

6

b)

8

c)

4

d)

10

24.

Find the value of y.

a)

22

b)

11

c)

5.5

d)

44

25.

Tell whether the angles are complementary or supplementary. Then find the value of x.

a)

Complementary; x=25

b)

Complementary; x=5

c)

Supplementary; x=25

d)

Supplementary; x=5

26.

Given D is between C and E, Use the segment addition postulate to solve for x.

a)

9

b)

0

c)

8

d)

-8

27.

M is the midpoint of AB. If AM = 5x+10 & MB = 4x+16, find the value of AM.

a)

6

b)

4

c)

70

d)

40

28.

Find the measure of angle B.

(a)

29.

A base angle of an isosceles triangle is 18 more than 4 times the vertex angle. Find the measure of one of the base angles.

(a)

30.

Find x

(a)

31.

What additional information is required for the 2 triangles to be congruent by ASA?

a)

A

b)

B

c)

C

d)

D

32.

What is the "statement" for step 3 of the proof?

a)

∡EDA≅∡DCB

b)

∡AED≅∡BEC

c)

DE=CE

d)

∡AED≅∡CED

33.

What is reason #3?

a)

SAS

b)

ASA

c)

SSS

d)

AAS

34.

What is statement #3?

a)

FH≅FH

b)

GF≅GF

c)

IH≅IH

d)

GF≅FI

35.

What trigonometric ratio would be used to find the distance from the ship to the plane?

a)

sine

b)

cosine

c)

tangent

d)

inverse sine

36.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.

a)

19 degrees

b)

45 degrees

c)

71 degrees

d)

138 degrees

37.

Find the Volume of this triangular prism.

a)

960 cm³

b)

240 cm³

c)

960 cm ²

d)

1920 cm³

38.

Find the volume of the figure. Round to the nearest tenth.

a)

80 cm³

b)

160 cm³

c)

42 cm³

d)

40 cm³

39.

How do you find the volume of a cylinder?

a)

V= ^1/₃πr²h

b)

V= ^4/₃πr²h

c)

V= ^4/₃πr³

d)

V= πr²h

40.

How do you find the volume of a sphere?

a)

V= ^1/₃πr²h

b)

V= ^4/₃πr²h

c)

V= ^4/₃πr³

d)

V= πr²h

41.

Which figure has a volume of 45π ft³?

a)

Cylinder with a height of 5ft and diameter of 6 ft

b)

Sphere with a radius of 3 ft

c)

Cone with a radius of 3 feet and height of 5 ft

d)

Sphere with a diameter of 5 feet

42.

A table tennis ball has a diameter of 40 mm. What is the approximate volume of the table tennis ball in cubic millimeters?

a)

1,676 mm³

b)

18,850 mm³

c)

33,510.3 mm³

d)

268,083 mm³

43.

What is the volume of the rectangular prism portion? (NUMBER, no units)

(a)

44.

A 3-inch wide ornament is placed in a box (3-inch). Sand is then poured around the ornament to keep it protected. How much sand is in the box? Select all that apply.

a)

$14.13in^3$

b)

$volume_{cube}-volume_{sphere}$

c)

$12.87in^3$

d)

$3^3-\left(\frac{4}{3}\pi\left(1.5^3\right)\right)$

45.

a)

$360.50\ cm^3$

b)

$190.85\ cm^3$

c)

$169.65\ cm^3$

d)

$551.35\ cm^3$

46.

What shape will the cross-section parallel to the base of a cone be?

a)

Dome

b)

Circle

c)

Pyramid

d)

Triangle

47.

What shape will the cross -section perpendicular to the base of a cylinder be?

a)

Circle

b)

Triangle

c)

Rectangle

d)

Ellipse

48.

What shape does this cross section cut perpendicular to the base make?

a)

Rectangle

b)

Circle

c)

Triangle

d)

Square

49.

Describe the cross section cut perpendicular to the base.

a)

rectangle

b)

square

c)

parallelogram

d)

circle

50.

A rectangle is a parallelogram

a)

Always

b)

Sometimes

c)

Never

51.

A parallelogram is a square

a)

Always

b)

Sometimes

c)

Never

52.

A quadrilateral is a parallelogram

a)

Always

b)

Sometimes

c)

Never

53.

A rhombus is a rectangle

a)

Always

b)

Sometimes

c)

Never

54.

The angles of a quadrilateral add up to 180 degrees.

a)

Always

b)

Sometimes

c)

Never

55.

The diagonals of a parallelogram are congruent

a)

Always

b)

Sometimes

c)

Never

56.

The opposite angles of a parallelogram are congruent

a)

Always

b)

Sometimes

c)

Never

57.

A rectangle has congruent diagonals

a)

Always

b)

Sometimes

c)

Never

58.

Find the measure of DG.

a)

14

b)

28

c)

12

d)

16

59.

Find the value of x.

a)

35

b)

3

c)

33

d)

None of these

60.

Find the value of x.

a)

23

b)

28

c)

30

d)

Cannot be determined

61.

What is the sum of measures of interior angles of a 23 gon?

a)

3460

b)

3620

c)

3780

62.

What is the sum of the measures of the exterior angles of a dodecagon?

a)

180

b)

360

c)

1440

d)

144

63.

If an interior angle of a regular polygon measures 144°, how many sides does it have?

a)

8

b)

9

c)

10

64.

Find the missing angle of the trapezoid.

a)

65

b)

115

c)

180

d)

None of these

65.

Find the value of x.

a)

7

b)

8

c)

85

d)

None of these

66.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

67.

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

68.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

Volume of 3D Shapes and Triangle Angles

Total questions: 68

Worksheet time: 6hrs 9mins

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