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Solid Figures. 7 th Grade Common Core Georgia Performance Standards: TCV.7.G.6 (3) Solve real-world and mathematical problems involving volume of cubes and right prisms. TCV.7.G.6 (2) Compute the surface area of right rectangular prisms and cubes in real-world and mathematical problems.

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Solid figures

Solid Figures

7th Grade Common Core Georgia Performance Standards:

TCV.7.G.6 (3) Solve real-world and mathematical problems involving volume of cubes and right prisms.

TCV.7.G.6 (2) Compute the surface area of right rectangular prisms and cubes in real-world and mathematical problems.

TCV.6.G.2 Find the volume of a right rectangular prism with fractional edge lengths. Discover and apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.TCV.6.G.4 (1) Represent three-dimensional figures using nets made up of rectangles and triangles.TCV.6.G.4 (2) Use nets to find the surface area of geometric figures in real-world and mathematical problems.

Gail Sherman 2013


Volume

What?

Huh?

Pardon Me?

Volume

  • CRCT Formula Sheet gives the following formula for the volume of rectangular prisms:

    V = area of base x h

  • Area of the base is just lw or length x width

  • h is the height, or how tall it is.


Volume of a rectangular prism
Volume of a Rectangular Prism

  • What is the shape of the base?

    • rectangle

  • Find area of the base.

    • 3x10 = 30

  • What is the height?

    • 5

  • Final Answer?

    • 3x10x5 = 150 units³

3

5

10


Your turn
Your Turn

5 in.

  • Find area of the base.

  • What is the height?

  • Final Answer?

4 in.

4 x 5 = 20

9 in.

9

(l x w) x h= (4x5) x 9 = 180in


Volume of a triangular prism
Volume of a Triangular Prism

  • What is the shape of the BIG B base?

    • triangle

  • Find the area of B.

    • (5x10)/2 = 25

  • What is the height?

    • 4

  • Final Answer?

    • 4(5x10)/2 = 100 units³

5

4

10


Nets

  • Draw a net of a cube.

  • How many faces?

6


Surface area of a cube
Surface Area of a Cube

  • Let’s name the faces of our cube.

    • Front

    • Back

    • Top

    • Bottom

    • Left

    • Right

      If each side is 3 inches long, find the surface area.


Add the areas of the 6 faces
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

2

4

7

Rectangular Prism

  • Just a box.

  • Draw a net for this rectangular prism.


How does your net compare

2

4

7

How does your net compare?

☺It’s ok to be different!☺

Now find the surface area.


2

4

7

.

Surface Area of a Rectangular Prism

.

  • Front =

  • Back =

  • Top =

  • Bottom =

  • Right =

  • Left =

  • Total =


Rectangular prism1

2

4

7

Rectangular Prism

  • Front = 4x7=28

  • Back = 4x7=28

  • Top = 2x7=14

  • Bottom = 2x7=14

  • Right = 2x4=8

  • Left = 2x4=8

  • Total = 100 units ²


Nets

  • Draw a net of a triangular prism.

  • How many faces?

4in.

2 in.

5 in.


Parts of the triangular prism
Parts of the Triangular Prism

Triangle

Triangle

Rectangle

Rectangle

Rectangle

4in.

2 in.

5 in.


Add the parts of the triangular prism
Add the Parts of the Triangular Prism

Triangle

Triangle

Rectangle

Rectangle

Rectangle

Total =

4in.

½bh= ½(5x4) =10

½bh= ½(5x4) =10

2 in.

lw=5x2 = 10

lw=5x2 = 10

5 in.

lw=5x2 = 10

50 in


Pyramid net
Pyramid Net

6 ft

  • Draw a net for the square pyramid

5 ft

5 ft


Use the net to name the parts of the pyramid
Use the net to name the parts of the pyramid.

6 ft

  • Square

  • Triangle

  • Triangle

  • Triangle

  • Triangle

5 ft

5 ft


Write formulas compute
Write Formulas & Compute

  • Square

  • Triangle

  • Triangle

  • Triangle

  • Triangle

25

15

15

15

15

85ft

lw =

½ bh=

½ bh=

½ bh=

½ bh=

5x5 =

½ (5x6)=

½ (5x6)=

½ (5x6)=

½ (5x6)=


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