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Math Major 124 (Plane and Solid Geometry)

Total questions: 50

Worksheet time: 44mins

Name
Class
Date
1.

Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides.

a)

441.66 cm2

b)

467.64 cm2

c)

519.60 cm2

d)

493.62 cm2

2.

A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the large pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon.

a)

430.70 cm3

b)

573.26 cm3

c)

473.77 cm3

d)

516.14 cm3

3.

The area of a circle is 89.42 sq. inches. What is the length of the side of a regular hexagon inscribed in a circle?

a)

5.533 in.

b)

5.335 in.

c)

6.335 in.

d)

7.335 in.

4.

A regular hexagon is inscribed in a circle whose diameter is 20 m. Find the area of the 6 segments of the circle formed by the sides of the hexagon.

a)

36. 45 sq. m

b)

63. 54 sq. m

c)

45. 63 sq. m

d)

54. 36 sq. m

5.

In triangle ABC, angle C = 70o, A= 45o, AB = 40 m. What is the length of the median drawn from vertex A to side BC?

a)

36.3 m

b)

36.6 m

c)

36.9 m

d)

37.2 m

6.

The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector?

a)

89.5 cm2

b)

58.9 cm2

c)

59.8 cm2

d)

85.9 cm2

7.

What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm?

a)

13.52

b)

14.18

c)

12.73

d)

1564

8.

Two complementary angles are in the ratio 2:1. Find the larger angle.

a)

30°

b)

60°

c)

75°

d)

15°

9.

One side of a parallelogram is 10 m and its diagonals are 16 m and 24 m, respectively. Its area is:

a)

156.8 sq. m.

b)

185.6 sq. m.

c)

158.7 sq. m.

d)

142.3 sq. m.

10.

The area of a rhombus is 132 square cm. if its shorter diagonal is 12 cm, the length of the longer diagonal is:

a)

20 centimeter

b)

21 centimeter

c)

22 centimeter

d)

23 centimeter

11.

A regular octahedron has an edge 2m. Find its volume (in m3).

a)

3.77

b)

1.88

c)

3.22

d)

2.44

12.

The central angle of a spherical wedge is 1 radian. Find its volume if its radius is 1 unit.

a)

2/3

b)

1/2

c)

3/4

d)

2/5

13.

The bases of a right prism is a hexagon with one of each side equal to 6 cm. The bases are 12 cm apart. What is the volume of the right prism?

a)

1211.6 cm3

b)

2211.7 cm3

c)

1212.5 cm3

d)

1122.4 cm3

14.

A circular cylinder with a volume of 6.54 cu. m is circumscribed about a right prism whose base is an equilateral triangle of side 1.25 m. What is the altitude of the cylinder in meters?

a)

3.50

b)

3.75

c)

4.00

d)

4.25

15.

The height of a right circular base down is h. If it contains water to depth of 2h/3 the ratio of the volume of water to that of the cone is:

a)

1:27

b)

2:3

c)

8:27

d)

26:27

16.

A conical vessel has a height of 24 cm. and a base diameter of 12 cm. It holds water to a depth of 18 cm. above its vertex. Find the volume of its content in cc.

a)

387.4

b)

381.7

c)

383.5

d)

385.2

17.

The slant height of a right circular cone is 5m long. The base diameter is 6m. What is the lateral area in sq. m?

a)

37.7

b)

47

c)

44

d)

40.8

18.

The base areas of a frustum of a cone are 25 sq. cm. and 16 sq. cm, respectively. If its altitude is 6 cm, find its volume.

a)

120 cm3

b)

122 cm3

c)

129 cm3

d)

133 cm3

19.

The surface area of the sphere is 4πr2. Find the percentage increase in its diameter when the surface area increases by 21%.

a)

5%

b)

10%

c)

15%

d)

20%

20.

If a solid steel ball is immersed in an eight cm. diameter cylinder, it displaces water to a depth of 2.25 cm. the radius of the ball is:

a)

3 cm

b)

6 cm

c)

9 cm

d)

12 cm

21.

A ___________is any closed, two-dimensional shape.

a)

quadrilateral

b)

figure

c)

plane figure

d)

solid figure

22.

A ______________ is three-dimensional, having length, width and height.

a)

plane figure

b)

solid figure

c)

triangle

d)

quadrilateral

23.

Any flat surface of a solid figure is called a ____.

a)

edge

b)

face

c)

vertice

d)

shape

24.

The line segment where two faces of a solid figure intersect is called ______.

a)

face

b)

vertex

c)

edge

25.

The point at which two or more lines, line segments, or rays meet to form an angle. In solid figures, a _______ is the point at which three or more faces meet.

a)

face

b)

edge

c)

vertex

26.

What shape am I?

I have one circle and one curved side. My curved side surface meets at a sharp point. I have no edges.

a)

cube

b)

sphere

c)

cone

d)

triangular prism

27.

What shape am I?

I have two congruent circles that are joined by a curved surface. I have no edges or vertices, but I can roll.

a)

Cylinder

b)

Sphere

c)

Cone

d)

Cube

28.

What shape am I?

I am round with no edges, vertices, or edges.

a)

Cyclinder

b)

Sphere

c)

Cone

d)

Circle

29.

What shape am I?

I have 6 faces , 12 edges, and 8 vertices. I have all the same shaped faces. All my edges are the same length.

a)

Square Pyramid

b)

Rectangular Prism

c)

Cube

d)

Cone

30.

What shape am I?

I have 12 edges, 8 vertices, and 6 faces. I have both square and rectangular faces.

a)

Rectangle

b)

Cube

c)

Square Pyramid

d)

Rectangular Prism

31.

What shape am I?

I have 5 faces, 8 edges, and 5 vertices. I have two different shaped faces.

a)

Square Pyramid

b)

Rectangular Prism

c)

Cube

d)

Cyclinder

32.

What geometric figure will be created?

a)

Cube

b)

Rectangular Prism

c)

Square Pyramid

d)

Cone

33.

What geometric shape will be created?

a)

Cube

b)

Rectangular Prism

c)

Squares

d)

Cyclinder

34.

What combinations of shapes would you need to create a cube?

a)

6 square faces

b)

6 rectangle faces

c)

4 squares and 2 rectangles faces

d)

4 rectangles and 2 square faces

35.

What combinations of shapes would you need to create a rectangular prism?

a)

6 square faces

b)

6 rectangle faces

c)

4 squares and 2 rectangles faces

d)

4 rectangles and 2 square faces

36.

(a)   is the sum of all the areas of the lateral faces and the base of the solid.

37.

The solid that has at least three faces that are rectangles is called (a)   .

38.

A prism has two bases while the pyramid has only (a)   base.

39.

(a)   refers to the 3-dimensional space enclosed by a surface.

40.
a)

They have the same volume.

b)

Cylinder A

c)

Cylinder B

d)

There is not enough information to determine.

41.

V=BhV=Bh  

S=Ph+2BS=Ph+2B  

The big B in the equations for volume and surface area means...

a)

The AREA of the BASE.

b)

The Circumference of the BASE.

c)

The PERIMETER of the BASE.

d)

the distance between the two bases.

42.
The volume of a cylinder of radius 'r' and height 'h' is
a)
π rh cu.unit
b)
2π rh cu.unit
c)
2π r h cu.unit
d)
π r h(r + h) cu.unit
43.
Shelby wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in. by 2 in. and the front and back are 8 in. by 2 in. How much wrapping paper will Chloe need to wrap the present?

Is this problem asking about Lateral or Total surface area?
a)
Lateral
b)
Total
44.

If all of the dimensions of a triangular prism decreased by 1/3, how much would the volume decrease by?

a)

1/27

b)

1/9

c)

1/3

d)

1/6

45.
What is the formula for the volume of a cone?
a)
V = (1/3)P*h
b)
V = (4/3)πr3
c)
V = πr2 + πrl
d)
V = (1/3)πr2h
46.
Is it possible for a cross section of a cylinder to have a triangular shape?
a)
yes
b)
no
c)
sometimes
47.

Describe the position of the plane.

a)

Vertical

b)

Horizontal

c)

Diagonal

48.

A right cylinder is cut perpendicular to its base. The shape of the cross section is a

a)

circle

b)

cylinder

c)

rectangle

d)

triangular prism

49.

A two-dimensional cross section is taken of a three-dimensional object. If this cross section is a triangle, what can not be the three-dimensional object?

a)
b)
c)
d)
50.
Describe the cross section.
a)
circle
b)
oval
c)
semi-circle
d)
trapezoid