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NUMBER THEORY: FINAL EXAMINATION 2024

Total questions: 100

Worksheet time: 5hrs 0mins

Name
Class
Date
1.

A ______ is a three-dimensional shape with a circular base and a single vertex. It's characterized by its height, radius, and slant height

a)

Cone

b)

Sphere

c)

Pyramid

d)

Cylinder

2.

Types of Cone are the following, except.

a)

Right Circular Cone

b)

Oblique Cone

c)

Elliptical Cone

d)

Traffic Cone

3.

What is the volume of the cone? Use 3.14 for π

a)

904.32

b)

301.44

c)

150.72

d)

288

4.

What is the volume of the cone? Use 3.14 for π

a)

150.72

b)

452.16

c)

1808.64

d)

602.88

5.

This shape is called a _______________________.

a)

Cylinder

b)

Cone

c)

Sphere

d)

Rectangular Prism

6.

What is the formula for the volume of a cone?

a)
b)
c)
d)
7.

What is the height of the cone?

a)

12 in

b)

6 in

c)

9 in

8.

What is the radius of the cone?

a)

2.5 cm

b)

4.8 cm

c)

5 cm

d)

10 cm

9.

A ______ is a perfectly symmetrical three-dimensional object where every point on its surface is equidistant from its center

a)

Cone

b)

Cylinder

c)

Sphere

d)

Prism

10.

Find the surface area of the sphere.

a)

48π mm2

b)

144π mm2

c)

72π mm2

d)

134π mm2

11.
Find the volume of this sphere.
a)
113 m³
b)
10.6 m³
c)
9.4 m³
d)
14.1 m³
12.

Find the surface area of the sphere.

a)

48π mm2

b)

144π mm2

c)

72π mm2

d)

134π mm2

13.

Formula in finding the surface area of the sphere.

a)

A=4πr2

b)

A=4πr3

c)

A= 43\frac{4}{3} πr3

d)

A= 43\frac{4}{3} πr2

14.

Formula in finding the total surface area of the cone.

a)

A​=πr(r+s)

b)

A​=πr2(r+s)

c)

A​=πr(r2+s)

d)

A​=r(r+s)

15.

Formula in finding the volume of a cone.

a)

V= 13\frac{1}{3} ​πr2h

b)

V= 43\frac{4}{3} ​πr2h

c)

V= 13\frac{1}{3} ​πr3h

d)

V= 13\frac{1}{3} ​πr2h2

16.

In ∆SIE, L and D are the midpoints of SI and IE respectively. If LD is 12, then what is the value of SE?

a)

SE = 48

b)

SE = 6

c)

SE = 24

d)

SE = 12

17.

In ∆BNS, O and U are the midpoints of BN and NS respectively. How will you compute the OU?

a)

OU=12BSOU=\frac{1}{2}BS

b)

OU=12USOU=\frac{1}{2}US

c)

OU=12BNOU=\frac{1}{2}BN

d)

OU=12ONOU=\frac{1}{2}ON

18.

Complete the segment:

The segments whose [1] ________ are the [2] ________ of a two sides of a triangle is [3] ________ to the third side and it has length equal to half the length of the third side.

a)

[1] midpoint, [2] endpoints, [3] parallel

b)

[1] endpoints, [2] midpoint, [3] congruent

c)

[1] midpoint, [2] endpoints, [3] congruent

d)

[1] endpoints, [2] midpoint, [3] parallel

19.

In ∆SIE, L and D are the midpoints of SI and IE respectively. If LI = 18, what is the value of LS?

a)

LS = 27

b)

LS = 36

c)

LS = 9

d)

LS = 18

20.

Name the pictured part of the circle.

a)

Radius

b)

Central Angle

c)

Sector

d)

Center

e)

Arc

21.

Name the pictured part of the circle.

a)

Radius

b)

Central Angle

c)

Sector

d)

Center

e)

Arc

22.

Name the pictured part of the circle.

a)

Center

b)

Sector

c)

Radius

d)

Central Angle

e)

Arc

23.

Name the pictured part of the circle.

a)

Radius

b)

Central Angle

c)

Sector

d)

Center

e)

Arc

24.

Name the pictured part of the circle.

a)

Diameter

b)

Sector

c)

Radius

d)

Central Angle

e)

Arc

25.

Name the pictured part of the circle.

a)

Diameter

b)

Sector

c)

Radius

d)

Central Angle

e)

Arc

26.

Name the pictured part of the circle.

a)

Diameter

b)

Sector

c)

Radius

d)

Chord

e)

Arc

27.

Name the pictured part of the circle.

a)

Diameter

b)

Sector

c)

Radius

d)

Chord

e)

Semicircle

28.
What is C?
a)
diameter
b)
center
c)
circumference
d)
radius
29.
What is the radius if the diameter is 12 m ?
a)
24 m
b)
6 m
c)
4 m
d)
48 m
30.
What is the diameter of a circle with a radius of 10 in?
a)
20
b)
5
c)
40
31.
If the diameter of a circle is 10 cm, the radius is 5 cm.
a)
TRUE
b)
FALSE
32.

What part of a circle does the red line represent?

a)

the radius

b)

the diameter

c)

the circumference

33.

Find the measure of arc AB.

a)

17 degrees

b)

34 degrees

c)

68 degrees

d)

146 degrees

34.

Solve for x

a)

51 degrees

b)

61 degrees

c)

102 degrees

d)

204 degrees

35.
This is a picture of ___________.
a)
Minor Arc
b)
Major Arc
c)
Semi-Circle
d)
Central Angle
36.
a)
Inscribed Angle
b)
Central Angle
37.
This is a picture of ___________.
a)
Minor Arc
b)
Major Arc
c)
Semi-Circle
d)
Central Angle
38.
inscribed angle: an angle with its vertex _____________ the circle
a)
at the center of
b)
on
39.
Solve for the missing angle.
a)
45o
b)
90o
c)
22.5o
d)
128o
40.
a)
A
b)
B
c)
C
d)
D
41.

Type of polyhedron characterized by having two parallel, congruent faces called bases, and other faces that are parallelograms.

a)

Cylinders

b)

Prisms

c)

Cone

d)

Pyramid

42.

Lucia has a triangular prism that has a length of 6 cm, a width of 4 cm, and a height of 8cm. What is the volume?

a)

96cm³

b)

54cm³

c)

80cm³

d)

24cm³

43.

Find the Volume of this triangular prism.

a)

960 cm 3

b)

240 cm 3

c)

960 cm 2

d)

1920 cm 3

44.
Find the total surface area of the prism.
a)
48 square inches
b)
64 square inches
c)
88 square inches
d)
76 square inches
45.
What is the area of the triangle?
a)
6 cm2
b)
12 cm2
c)
18 cm2
d)
588 cm2
46.
 Find the volume of the Cylinder
a)
7230
b)
6621
c)
1130
d)
907
47.
Find the Volume if the height is 10 cm and radius 3 cm?
a)
250
b)
200
c)
283
d)
180
48.
Find the Volume of the Cylinder
a)
1178 ft3
b)
4712 ft3
c)
7069 ft3
d)
3534 ft3
49.
Michael has a very large soup pot shaped like a cylinder that has a height of 15  inches and a radius of 6 inches. How much soup can Michael’s soup pot hold?
a)
4239 in3
b)
423.9 in3
c)
1695.6 in3
d)
 1695.6 in2
50.
Which cylinder will have a larger volume?
a)
Cylinder A
b)
Cylinder B
51.
In the following image what does A represent?
a)
Face
b)
Vertex
c)
Edge
52.
In the following image what does C represent?
a)
Face
b)
Vertex
c)
Edge
53.
In the following image what does "This is called" represent?
a)
Face
b)
Vertex
c)
Edge
54.

Which unit is NOT appropriate for volume.

a)
square miles
b)
inches3
c)
cm3
d)
cubic feet
55.
Find the Surface Area
a)
556 cm2
b)
278 cm2
c)
680 cm2
d)
340 cm2
56.

Types of Cylinder, except.

a)

Right Cylinder

b)

Oblique Cylinder

c)

Elliptic Cylinder

d)

Hydraulic Cylinder

57.

A geometric shapes with straight parallel sides and circular or oval cross-sections

a)

Cylinders

b)

Prisms

c)

Cube

d)

Spheres

58.

Properties of a cylinders, except

a)

Axis

b)

Height

c)

Base Radius

d)

Lateral faces

59.

Cylinder in real life, except

a)

Cans

b)

Pipes

c)

Tanks

d)

Cube

60.

Formulas for a Right Circular Cylinder, except

a)

Volume

b)

Total Surface Area

c)

Lateral Surface Area

d)

Lateral Face

61.
Find the Surface Area
a)
15m2
b)
16m2
c)
18m2
d)
20m2
62.
A pyramid has a square base. Each side of the base is 9 cm. The slant height of each triangle is 14 cm. What is the surface area?
a)
126 cm2
b)
144 cm2
c)
252 cm2
d)
333 cm2
63.
What is the volume of the following triangular pyramid?
a)
3400 cubic in
b)
566.67 cubic in
c)
1133.33 cubic in
d)
1700 cubic in
64.
What is the volume of the following rectangular pyramid?
a)
990 cubic inches
b)
495 cubic inches
c)
660 cubic inches
d)
330 cubic inches
65.
What is the volume of the following rectangular pyramid?
a)
8085 cubic meters
b)
5390 cubic meters
c)
16170 cubic meters
d)
10780 cubic meters
66.
A sign made of solid wood is in the shape of a pyramid. The base is a triangle with a base of 6 feet and a height of 4 feet. The height of the sign
is 7 feet. The wood costs $3 per cubic foot. What is the cost of the sign?
a)
$168
b)
$56
c)
$84
d)
$28
67.
A triangular pyramid has a base with an area of 9cm2. Each lateral face has a base of 5cm and a height of 4cm. Find the total surface area.
a)
29cm2
b)
69cm2
c)
40cm2
d)
39cm2
68.
Find the lateral area and surface area of each figure. Round your answers to the nearest tenth, if necessary.
a)
152.6 cm²; 187.7 cm²
b)
212 ft²; 322 ft²
c)
219.6 in²; 313.2 in²
d)
50.4 in²; 66.4 in²
69.
Find the lateral area and surface area of each figure. Round your answers to the nearest tenth, if necessary.
a)
219.6 in²; 313.2 in²
b)
50.4 in²; 66.4 in²
c)
152.6 cm²; 187.7 cm²
d)
212 ft²; 322 ft²
70.
Find the lateral area and surface area of each figure. Round your answers to the nearest tenth, if necessary.
a)
212 ft²; 322 ft²
b)
152.6 cm²; 187.7 cm²
c)
219.6 in²; 313.2 in²
d)
50.4 in²; 66.4 in²
71.
What is the formula for Volume of a Cone?
a)
V=π r3h
b)
V=π r2h
c)
V=(1/3)π r2h
d)
V=(4/3)π r3
72.
V = ?
a)
14.13 in3
b)
56.52 in3
c)
169.56 in3
73.
Find the volume of the figure.
a)
150.72 cm³
b)
75.36 cm³
c)
452.16 cm³
d)
151 cm³
74.
Find the volume of the cone. (Round to the nearest integer.)
a)
1810 in³
b)
151 in³
c)
452 in³
d)
276 in
75.
a)
400
b)
1200
c)
3600
d)
324
76.

A paper party hat, like the one shown, has a slant height of 6 inches and a radius of 5 inches. How many square inches of cardboard would be needed to create this hat?

a)

94.25 in.2

b)

172.79 in.2

c)

50 in.2

d)

22.5 in.2

77.
What is the shape of the base of a cone?
a)
Rectangle
b)
Triangle
c)
Square
d)
Circle
78.
Find the surface area of the cone. Round your answers to the nearest tenth. 
a)
282.7 in3
b)
314.2 in3
c)
309.2 in3
d)
267.4 in3
79.

Prism or Pyramid?

a)

Prism

b)

Pyramid

80.

Prism or Pyramid?

a)

Prism

b)

Pyramid

81.

Which one has 1 base...Prism or Pyramid??

a)

Prism

b)

Pyramid

82.

Which one has 2 bases...Prism or Pyramid??

a)

Prism

b)

Pyramid

83.

Prism or Pyramid??

a)

Prism

b)

Pyramid

84.

Prism or Pyramid??

a)

Prism

b)

Pyramid

85.

Name this figure.

a)

Square Pyramid

b)

Triangular Prism

c)

Square Prism

d)

Triangular Pyramid

86.

Prism or Pyramid??

a)

Prism

b)

Pyramid

87.

Prism or Pyramid?

a)

Prism

b)

Pyramid

88.

Prism or Pyramid?

a)

Prism

b)

Pyramid

89.

Prism or Pyramid?

a)

Prism

b)

Pyramid

90.

What 3-D shape is this?

a)

Triangular Prism

b)

Rectangular Prism

c)

Triangular Pyramid

d)

Rectangular Pyramid

91.
What 3-D shape is this?
a)
Triangular Prism
b)
Rectangular Pyramid
c)
Cube
d)
Square
92.
What 3-D shape is this?
a)
Cube
b)
Rectangular Pyramid
c)
Rectangular Prism
d)
Triangular Prism
93.
What 3-D shape is this?
a)
Triangular Pyramid
b)
Triangular Prism
c)
Rectangular Pyrramid
d)
Cube
94.

Which one doesn't belong?

a)

A

b)

B

c)

C

d)

D

95.

Which shape best fits into this group?

a)
b)
96.

All these shapes are pyramids. True or false?

a)

True

b)

False

97.

Select all prism shapes:

a)
b)
c)
d)
e)
98.

Trevor and Matt each build a three dimensional figure as shown. Who built a pyramid?

a)

Trevor

b)

Matt

c)

Neither

d)

Both

99.

What formula represents the volume of a cone?

a)
b)
c)
d)
100.

What formula represents volume of a sphere?

a)
b)
c)
d)

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