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3D Figures & Proportional Solids Review

Total questions: 70

Worksheet time: 6hrs 19mins

Name
Class
Date
1.

A rectangle and a horizontal line segment are shown. What is the resulting object when the rectangle is rotated around the horizontal line segment?

a)
b)
c)
d)
2.

The right triangle as shows is rotated 360° about

the y-axis in three dimensions. What is the

3-Dimensional solid resulting from the rotation?

a)

cone

b)

cylinder

c)

pyramid

d)

prism

3.

Select the 2D object that can be rotated to form the 3D object shown.

a)
b)
c)
d)
4.

Which 3-D solid is created when the rectangle is rotated about the horizontal line?

a)
b)
c)
d)
5.

Which 2-D shape could be revolved about the vertical line to create the 3-D solid?

a)
b)
c)
d)
6.
What cross-section is formed by slicing through a cube perpendicular to any face?
a)
rectangle
b)
square
c)
parallelogram
d)
triangle
7.
What cross sections might you see when a plane intersects a cone that you would not see when a plane intersects a pyramid or a prism?
a)
circle
b)
trapezoid
c)
rectangle
d)
trapezoid
8.
What shape will the horizontal cross-section of a sphere be?
a)
Dome
b)
Circle
c)
Ellipse
d)
Rectangle
9.
Describe the cross section.
a)
triangle
b)
rectangle
c)
oval
d)
trapezoid
10.
Describe the cross section.
a)
rectangle
b)
trapezoid
c)
oval
d)
parallelogram
11.
Describe the cross section.
a)
trapezoid
b)
triangle
c)
rectangle
d)
square
12.
Is it possible for a cross section of a cylinder to have a triangular shape?
a)
yes
b)
no
c)
sometimes
13.
Describe the cross section.
a)
circle
b)
oval
c)
semi-circle
d)
trapezoid
14.

Rotating this triangle around line AB creates a ____________.

a)

triangle

b)

triangular prism

c)

triangular pyramid

d)

cone

15.

Rotating this rectangle around line AB creates a ____________.

a)

rectangle

b)

rectangular prism

c)

cylinder

d)

cone

16.

Rotating this circle around the diameter creates a ____________.

a)

pyramid

b)

sphere

c)

cylinder

d)

cone

17.

Rotating this rectangle around line BD create a cylinder with:

a)

height 15 and radius 8

b)

height 15 and radius 4

c)

height 8 and radius 15

d)

height 8 and radius 7.5

18.

Rotating this rectangle around line AB create a cylinder with:

a)

height 15 and radius 8

b)

height 15 and radius 4

c)

height 8 and radius 15

d)

height 8 and radius 7.5

19.

Rotating this triangle around the side labeled "5" will create cone with the dimensions:

a)

height: 5 and radius: 12

b)

height: 5 and radius: 24

c)

height: 12 and radius: 5

d)

height: 12 and radius: 10

20.

Rotating this triangle around the side QR will create cone with the dimensions:

a)

height: 8 and radius: 6

b)

height: 8 and radius: 3

c)

height: 3 and radius: 8

d)

height: 6 and radius: 8

21.

Which three-dimensional figure will result when a rectangle 6 inches long and 5 inches wide is continuously rotated about the longer side?

a)

a rectangular prism with a length of 6 inches, width of 6 inches, and height of 5 inches

b)

a rectangular prism with a length of 6 inches, width of 5 inches, and height of 5 inches

c)

a cylinder with a radius of 5 inches and a height of 6 inches

d)

a cylinder with a radius of 6 inches and a height of 5 inches

22.

When you stack congruent rectangles, what 3D figure is created?

a)

Rectangular Prism

b)

Rectangular Pyramid

c)

Cylinder

d)

Cone

23.

When you stack congruent triangles, what 3D figure is created?

a)

Triangular Prism

b)

Triangular Pyramid

c)

Rectangular Pyramid

d)

Cone

24.

When you stack similar triangles, what 3D figure is created?

a)

Triangular Prism

b)

Triangular Pyramid

c)

Rectangular Pyramid

d)

Cone

25.

When you stack similar rectangles, what 3D figure is created?

a)

Triangular Prism

b)

Triangular Pyramid

c)

Rectangular Pyramid

d)

Cone

26.

When you stack similar circles, what 3D figure(s) is created?

a)

Prism

b)

Cylinder

c)

Sphere

d)

Cone

27.

When you stack congruent circles, what 3D figure is created?

a)

Prism

b)

Cylinder

c)

Sphere

d)

Cone

28.
The fish tank in the library is 3 feet long, 5 feet wide, and 4 feet deep.  What is the volume of the fish tank?
a)
15 cu ft
b)
20 cu ft
c)
60 cu ft
d)
15 cu ft
29.
Mrs. Dunnahoo has a Finding Dory tissue box on her desk.  The box has a base of 8.4 in2  and a height of 5 inches.  what is the volume of the tissue box in cubic inches?
a)
42 in3
b)
40.20 in3
c)
45 in3
d)
42.1 in3
30.
Find the volume of the cylinder.
a)
4239
b)
1696
c)
1130
d)
565
31.
A cylindrical carton of oatmeal has a diameter of 13 cm and is 24 cm tall.  Find the volume.
a)
12742.3 cubic cm
b)
3185.6 cubic cm
c)
3452 cubic cm
d)
8345 cubic cm
32.
Find the volume of this shape
a)
1520.53
b)
276.46
c)
552.93
d)
6082.12
33.
Which cylinder will have a larger volume?
a)
Cylinder A
b)
Cylinder B
34.
Calculate the volume of the pyramid in the picture.  Round to the nearest whole number if necessary.
a)
216 yd3
b)
108 yd3
c)
72 yd3
d)
36 yd3
35.
Calculate the volume of the pyramid in the picture.  Round to the nearest whole number if necessary.
a)
160 in3
b)
960 in3
c)
480 in3
d)
320 in3
36.
Calculate the volume of the pyramid in the picture.  Round to the nearest whole number if necessary.
a)
120 ft3
b)
96 ft3
c)
288 ft3
d)
 192 ft3
37.
Find the volume of the figure.
a)
1,800 cm³
b)
900 cm³
c)
600 cm³
d)
750 cm³
38.
Find the volume of the figure.
a)
150.72 cm³
b)
75.36 cm³
c)
452.16 cm³
d)
151 cm³
39.
a)
42.4 in3
b)
169.6 in3
c)
56.5 in3
d)
14.13 in3
40.
Find the volume of the cone. (Round to the nearest integer.)
a)
1810 in³
b)
151 in³
c)
452 in³
d)
276 in
41.
a)
1,767 ft3
b)
7,068.5 ft3
c)
589 ft3
d)
4,417.9 ft3
42.

What is the LATERAL SURFACE AREA of the cylinder?

a)

282.6

b)

635.85

c)

28.26

d)

353.25

43.

Find the TOTAL SURFACE AREA of the cylinder

a)

493.16

b)

177.18

c)

354.37

d)

211.88

44.

What is the LATERAL SURFACE AREA of the cylinder?

a)

552.64

b)

1036.2

c)

276.32

d)

466.29

45.

What is the LATERAL SURFACE AREA of the cylinder?

a)

753.6

b)

401.92

c)

1155.52

46.
A square pyramid is covered with decorative wrapping paper with no overlap.  The net of the box is shown on the right.  How many square centimeters of wrapping paper are needed to cover the surfaces of the box? 
a)
108 cm2
b)
324 cm2
c)
180 cm2
d)
432 cm2
47.
What is the total surface area of the rectangular pyramid whose net is shown?
a)
400 in2
b)
800 in2
c)
1,200 in2
d)
1,600 in2
48.
Find the total surface area of the figure.
a)
500 ft2
b)
515 ft2
c)
525 ft2
d)
510 ft2
49.
What is the lateral area of the prism?
a)
299 units2
b)
21 units2
c)
320 units2
d)
 784.9 units2
50.
Find the lateral surface area of the prism.
a)
25 square inches
b)
37.5 square inches
c)
136 square inches
d)
95.5 square inches
51.

What is the surface area?

a)

6658.56 mm2

b)

452.16 mm2

c)

904.32 mm2

d)

108.8 mm2

52.

Determine the volume of the cone shown:

a)

2093 ft3

b)

6280 ft3

c)

2000 ft3

d)

667 ft3

53.

Determine the surface area of the cone shown.

a)

173.3 ft2

b)

296.6 ft2

c)

89.5 ft2

d)

223.7 ft2

54.

Determine the surface area of the cone shown. Use 3.14 for pi. Round to the nearest whole number. Do not enter units.

(a)  

55.
A living room is 20 feet long, 50 feet wide, and 12 feet high.  How much paint do you need to cover the walls?
a)
1680 feet 2
b)
2680 feet 2
c)
3680 feet 2
d)
4680 feet 2
56.
A solid ball with a diameter of 2 inches is dropped into a cup with a diameter of 3 inches and a height of 8 inches. Assuming the ball cannot absorb liquid and will sink to the bottom of the cup, what volume of water can the cup now hold? 
a)
76 cu in
b)
26  cu in
c)
104 cu in
d)
52 cu in
57.

The surface area of a rectangular prism is 166 square feet. A similar prism has a surface area of 1494 square feet. If the length of the smaller prism is 5 feet, what is the length of the larger prism?

a)

10

b)

15

c)

45

d)

50

58.
Find the volume of the larger solid given the information below.
V = 125 m3
V = ? m3

SA = 200 m2
SA = 288  m2
a)
150
b)
180
c)
200
d)
216
59.

Each pair of figures is similar. Use the information given to find the scale factor of the figure on the left to the figure on the right.

a)

1 : 63

b)

7 : 9

c)

49 : 81

d)

343 : 729

60.

Each pair of figures is similar. Use the information given to find the scale factor of the figure on the left to the figure on the right.

a)

1 : 10

b)

40 : 1

c)

4 : 25

d)

2 : 5

61.

Each pair of figures is similar. Use the information given to find the scale factor of the figure on the left to the figure on the right.

a)

1 : 7

b)

7 : 10

c)

49 : 100

d)

343 : 1000

62.

The two figures are similar. Find the scale factor of the figure on the left to the figure on the right. Then find the ratio of surface areas and the ratio of volumes.

a)

9:8, 81:64, 729:512

b)

9:8, 9:4, 27:8

c)

9:8, 729:512, 81:64

d)

9:17, 729:289, 81:4913

63.

The scale factor between two similar figures is given. The surface area and volume of the smaller figure are given. Find the surface area and volume of the larger figure.

a)

SA = 384 ft2, V = 576 ft3

b)

SA = 128 ft2, V = 256 ft3

c)

SA = 128 ft2, V = 1024 ft3

d)

SA = 512 ft2, V = 1024 ft3

64.

The surface area of a rectangular prism is 166 square feet. A similar prism has a surface area of 1494 square feet. If the length of the smaller prism is 5 feet, what is the length of the larger prism?

a)

10

b)

15

c)

45

d)

50

65.

Two similar cylinders have surface areas of 40π ft2 and 90π ft2. What is the ratio of the height of the large cylinder to the height of the small cylinder?

a)

4/9

b)

2/3

c)

8/27

d)

16/81

66.
Two spheres have a similarity ratio of 1:3.  The smaller sphere has a surface area of 16 ft2.  What is the surface area of the larger sphere.
a)
48 ft2
b)
144 ft2
c)
432 ft2
d)
32 ft2
67.
The surface area of the larger prism is 2560 m2.  Find the surface area of the smaller prism.
a)
921.6 m2
b)
1536 m2
c)
553 m2
d)
7111.1 m2
68.

What is the surface area of the larger solid?

a)

50 ft2

b)

45 ft2

c)

81 ft2

d)

225 ft2

69.

What will the surface area of the smaller cone be?

Enter a number only.

(a)  

70.

What will the surface area of the smaller cone be?

Enter a number only.

(a)  

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