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. 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  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. Pardon Me?

Volume of a Rectangular Prism     What is the shape of the base?

 rectangle Find area of the base.

3  3x10 = 30 5 What is the height?

 5 10 Final Answer?

 3x10x5 = 150 units³

Your Turn    Find area of the base.

4 x 5 = 20 What is the height?

9 Final Answer?

(l x w) x h= (4x5) x 9 = 180in

5 in

.

Volume of a Triangular Prism     What is the shape of the BIG B base?

 triangle

5

Find the area of B.

 (5x10)/2 = 25

4 10

What is the height?

 4 Final Answer?

 4(5x10)/2 = 100 units³

Nets   Draw a net of a cube. How many faces?

6

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!

       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?

2 4 7 ☺ It’s ok to be different!

☺ Now find the surface area.

.

Surface Area of a Rectangular Prism .

 Front =  Back =  Top =  Bottom =  Right =  Left =  Total = 4 2 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 4 2 7

Nets   Draw a net of a triangular prism. How many faces?

4in.

Parts of the Triangular Prism Triangle Triangle Rectangle Rectangle Rectangle 4in.

Add the Parts of the Triangular Prism Triangle ½bh= ½(5x4) =10 Triangle ½bh= ½(5x4) =10 Rectangle Rectangle lw=5x2 = 10 lw=5x2 = 10 Rectangle lw=5x2 = 10 Total = 50 in 4in.

Pyramid Net  Draw a net for the square pyramid 5 ft

6 ft

Use the net to name the parts of the pyramid.

6 ft

 Square  Triangle  Triangle  Triangle  Triangle 5 ft

Write Formulas & Compute      Square Triangle Triangle Triangle Triangle lw = ½ bh= ½ bh= ½ bh= ½ bh= 5x5 = ½ (5x6)= ½ (5x6)= ½ (5x6)= ½ (5x6)= 25 15 15 15 15 85ft