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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 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.
Huh?
What
?
Pardon Me?
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
10
5
Your Turn
Find area of the base.
What is the height?
Final Answer?
4 in
. 5 in.
9 in
.
4 x 5 = 20
9
(l x w) x h= (4x5) x 9 = 180in
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
410
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 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 =
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.
5 in.
2 in.
Parts of the Triangular Prism
TriangleTriangleRectangleRectangleRectangle
4in.
5 in.
2 in.
Add the Parts of the Triangular Prism
Triangle Triangle Rectangle Rectangle RectangleTotal =
4in.
5 in.
2 in.
½bh= ½(5x4) =10
½bh= ½(5x4) =10
lw=5x2 = 10
lw=5x2 = 10
lw=5x2 = 10
50 in
Pyramid Net
Draw a net for the square pyramid
5 ft5 ft
6 ft
Use the net to name the parts of the pyramid.
Square
Triangle
Triangle
Triangle
Triangle
5 ft5 ft
6 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)=
2515151515
85ft