Prisms Lesson 8-2

2 Truths and a fib! A cylinder is not a polyhedron. 2. A cube is a type of pyramid. 3. A square pyramid has 5 faces.

What is a prism? A prism is a 3D figure with parallel bases that are polygons. The other faces of a prism are parallelograms, most often rectangles. The name of a prism tells what the base should be shaped like: – Triangular prism – triangle bases – Rectangular prism – rectangle bases – Cube – square bases – Pentagonal prism – pentagon bases

The base has sides. 4 Vertices (points) 8 Edges (lines) 12 Rectangular Prism The base has sides. 4 Vertices (points) 8 Edges (lines) 12 Faces (planes) 6

Vertices (points) 6 Edges (lines) 9 Faces (planes) 5 Triangular Prism The base has __ sides. 3 5

The base has sides. 6 Vertices (points) 12 Edges (lines) 18 Hexagonal Prism The base has sides. 6 Vertices (points) 12 Edges (lines) 18 Faces (planes) 8

The base has sides. 5 Vertices (points) 10 Edges (lines) 15 Pentagonal Prism The base has sides. 5 Vertices (points) 10 Edges (lines) 15 Faces (planes) 7

Name Picture Base Vertices Edges Faces Triangular Prism Rectangular Prism Pentagonal Prism Hexagonal Prism Heptagonal Prism Octagonal Prism 3 6 9 5 4 8 12 6 5 10 15 7 6 12 18 8 Draw it 7 14 21 9 8 16 24 10 No picture Any Prism n 2n 3n n+2

Volume of a Prism = Bh where B = Area of the Base and h = Height of the Prism Remember: the bases are the parallel sides and the height is the distance between the bases!!! Height of the prism Base

Volume of a Cube Volume= area of base x height V = Bh (B= AREA of the base) Side length is 5 inches Area of the base=? Height=? Volume= ? Area of the base=5(5) =25 Height=5 Volume= 125 cubic inches

Volume of a Rectangular Prism V = area of base x height V = Bh (B= AREA of the base) 5 4 8 Area of base =? Height = ? Volume = ? Area of base =5 x 4 = 20 H = 8 V = 20 x 8 = 160

Triangular Prism Volume 6 8 5 10 4 Volume = Bh Volume = area of base x height Area of the base=? Triangle ½(6)(4) =12 Height of prism= ? Height of prism= 10 Volume= (12)10=120 cubic units

Recall the concept of density, so we can apply this to real life problems.   A big theater in New York has 1.3 million square feet. At the last show a band named Flaming Bananas surveyed the theater to make sure there wasn’t overcrowding. They found the population density to be 0.015 people per square foot. This included all people in the building. How many total people attended the theater on that day?

Julia runs a hotel. She wants to hold a party in the banquet hall of her hotel. The hall has a size of 70,000 square feet. She found the population density to 0.004 people per square foot. This included all people in the banquet hall. How many total people can attend the party in banquet hall? 280 people

Look at cross-sections of a cube. Suppose a plane intersects a cube. Describe the different cross sections when a plane intersects a cube. Bryant says that it’s not possible to form a circle or an octagon as a cross section of a cube. Is Bryant correct? Explain your reasoning.

A rectangle What do you call a broken angle? Now try the “summer is coming soon” problem.

9900 =330(30)=9900 or 20 37.5 .625(60)=37.5