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. 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

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

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

How does your net compare? ☺ 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. 5 in. 2 in.

Parts of the Triangular Prism Triangle Rectangle 4in. 5 in. 2 in.

Add the Parts of the Triangular Prism Triangle Rectangle Total = 4in. 5 in. 2 in. ½bh= ½(5x4) =10 lw=5x2 = in

Pyramid Net  Draw a net for the square pyramid 5 ft 6 ft

Use the net to name the parts of the pyramid.  Square  Triangle 5 ft 6 ft

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