Solid Figures

6th Grade Georgia Performance Standards:

M6M3 Students will determine the volume of fundamental solid figures (right rectangular prisms, cylinders, pyramids, and cones).

M6M4 Students will determine the surface area of solid figures (right rectangular prisms and cylinders).

Gail Sherman 2010

Volume CRCT Formula Sheet

gives the following formula for the volume of all right solid figures:

V = Bh Big B stands for the

area of the base. Small b stands for the

base of a plane figure, like a triangle.

Very confusing.

Huh?

What

?

Pardon Me?

Volume of a Rectangular Prism

What is the shape of the BIG B base? rectangle

Find the area of B. 3x10 = 30

What is the height? 5

Final Answer? 3x10x5 = 150 units³

3

10

5

Volume of a Cylinder

What is the shape of B? circle

Find the area of B. π x 4² = 16

What is the height? 9

Final answer? π x 4² x 9 = 144π

9

4

Volume of a Cone This cone & cylinder have the same size bases

and they are the same height. Do they both hold the same amount of water?

Which one holds more?

How much more?

Let’s experiment…

Volume of a Cone You know that cylinder volume = Bh.

You know a cone is 1/3 the volume of a cylinder.

So…Volume of a cone is:

3

BhV

Volume of a Cone Find the volume of

the cone. Radius is 5. Height is 4

3

BhV

2 25 4 100 133

3 3 3 3

r hV

Nets

Draw a net of a cube. How many faces?

Surface Area of a Cube Let’s name the faces of our cube.

Front Back Top Bottom Left RightIf each side is 3 inches long, find the

surface area.

Add the areas of the 6 faces!

Front is…… 3x3=9 Back is……. 3x3=9 Top is……… 3x3=9 Bottom is… 3x3=9 Left is……… 3x3=9 Right is……. 3x3=9 And the TOTAL is 54 in²

Rectangular Prism

Just a box. Draw a net for this rectangular prism.

4

2

7

How does your net compare?

☺ It’s ok to be different! ☺

Now find the surface area.

4

2

7

.

.

Surface Area of a Rectangular Prism

Front = Back = Top = Bottom = Right = Left = Total =

Rectangular Prism

Front = 4x7=28 Back = 4x7=28 Top = 2x7=14 Bottom = 2x7=14 Right = 2x4=8 Left = 2x4=8 Total = 100 units ²

Do You See Any Shortcuts?

S.A. =2(lw+lh+wh) S.A. = 2wl+2hl+2wh

Cylinders

Draw a net of a soup can.

Net of a Cylinder

☺ It’s ok to be different! ☺

Find Surface area

If the soup can is 10 inches tall and has a radius of 3 inches.

10

3

Hints…

Look back at your net 2 circles

What’s that formula again? 1 rectangle

I know the height What is the width?

Add the parts together

Voila!

πr² gives me area of a circle. 3.14 x 3 x 3 = I have 2 of them, so I’ll multiply that by 2 =

2πr gives me circumference (width of rectangle) 2 x 3.14 x 3 x 10 = 188.4

Top = 28.26Bottom = 28.26Rectangle = 188.4TOTAL = 244.92 in²

Answering With Pi Sometimes there is no need to compute pi,

because they want the answer to be precise and contain pi.

In that case: πr² = π x 3² = 9π 2πr = 2 x π x 3 x 10 = 60π 9π + 9π + 60π = 78π