Lesson 6 Notes

Draw a few prisms on the board.

Notes

• In a prism, and at times in cylinders the shape is made by stacking several figures on top of each other that are similar.
• If you stacked the same shape as the base, except that it is a little smaller each time until they reached a point at the top, you will create what is known as a pyramid.
• These pyramids are named according to the shape of their base.
• The Great Pyramids of Egypt are square pyramids.

Prisms

• A prism has two bases that are congruent to each other.
• The two bases in a prism are parallel to each other.

Pyramids

• A pyramid has triangular sides and a rectangular or triangular base.
• A pyramid has one base, and is made of shapes similar to the base, that get progressively smaller until they come to a point called the apex.

Cross Sections

• A slice of any 3 dimensional figure with a plane creates a cross section.
• Cross sections are either taken parallel or perpendicular to the base.
• They can be taken at a diagonal as well.

Types of Cross Sections

• If a shape is cut parallel to the base, then the cross section looks just like the base.
• If a shape is cut perpendicular to the base, then the cross section looks just like the lateral face.
• If the shape is cut diagonally, the cross section looks like a stretched out base.

Volumes of Pyramids

V = ¹/₃Bh, where B is the base area.

Volume of a Rectangular Prism

V = lwh

Volumes of other prisms

V = Bh, where B is the area of the base.

Volumes of cones

V = πr²h ÷ 3.

Volume of a cylinder

V = πr²h