SOLID GEOMETRY III

Solid Geometry is the geometry of three-dimensional space, the kind of space we live in ...

Three Dimensions

It is called three-dimensional, or 3D because 

there are three dimensions:width, depth and height

 Cube (Hexahedron)

• It has 6 Faces  
• Each face has 4 edges, and is actually a square
• It has 12 Edges
• t has 8 Vertices (corner points)
• Surface Area = 6 × (Edge Length)²
• ^{Volume = (Edge Length)3}

Cylinder

• It has a flat base and a flat top
• The base is the same as the top, and also in-between
• It has one curved side
• Surface Area = 2 × π × r × (r+h)
• Volume = π × r² × h

Cone

• It has a flat base
• It has one curved side
• Surface Area of Base = π × r
• Surface Area of Side = π × r × s
• Volume = π × r² × (h/3)

Sphere

• It is perfectly symmetrical
• It has no edges or vertices (corners
• All points on the surface are the same distance from the center
• Surface Area = 4 × π × r²
• Volume = (4/3) × π × r³

YOUR TURN :

Question 1

What is the volume of a cube of edge length 4 cm?

A

64 cm³

B

96 cm³

C

128 cm³

D

256 cm³

Question 2

A cube has edge length 5 cm
What is its surface area?

A

125 cm²

B

150 cm²

C

250 cm²

D

900 cm²

Question 3

The diagram shows a cylinder of height 10 inches and radius 7 inches. What is its volume?

A

748 in³

B

1,496 in³

C

1,540 in³

D

2,200 in³

Question 4

An ice cream cone has vertical height 6 in and the diameter of its top is 3.5 in.
How many fluid ounces of ice cream does it hold when filled level with the top?

A

42.6

B

21.3 fluid ounces

C

18.3 fluid ounces

D

10.7 fluid ounces

Question 5

The diagram shows a cone of height 5 cm and base radius 12 cm.
What is the total surface area of side and base?
Use π = 3.14

A

282.60 cm²

B

568.34 cm²

C

656.26 cm²

D

942.00 cm²

Question 6

What is the volume of a sphere of radius 6 inches?

A

144π in³

B

288π in³

C

384π in³

D

512π in³

Question 7

The diagram shows the cross section of a rubber soccer ball of outside diameter 22 cm. The thickness of the rubber is 0.5 cm
What is the volume of the rubber to the nearest cm³?

A

372 cm³

B

726 cm³

C

4,849 cm³

D

5,575 cm³

Question 8

The diagram shows a cylinder of height 6 cm and radius 6 cm. What is its volume?
Use π = 3.14

A

226.08 cm³

B

452.16 cm³

C

678.24 cm³

D

1,356.48 cm³

Question 9

The diagram shows a cylindrical water tank of diameter 14 ft and height 8 ft

How many gallons (US liq) of water does the tank hold when full?
Use π = 22/7

To convert from ft³ to gallons (US liq) use the Unit Conversion Tool
at http://www.mathsisfun.com/unit-conversion-tool.php

A

2,633 gallons

B

7,674 gallons

C

7,920 gallons

D

9,216 gallons

Question 10

The volumes of the cube and the cone are equal. Express h in terms of r.

A

h = r²

B

h = 3r²/π

C

h = 3r/π

D

h = 3rπ