9-2A Volume of Prisms9-2A Volume of Prisms

What is volume?What is volume?

What question must you ask before What question must you ask before you can begin finding the volume of a you can begin finding the volume of a

prism?prism?

DefinitionDefinition

His mom yelled at him to turn the His mom yelled at him to turn the volume volume down on his playstation.down on his playstation.

The The volumevolume of the bottle was two liters. of the bottle was two liters.

The The volumevolume of a solid is the number of of a solid is the number of cubic units contained in the solid.cubic units contained in the solid.

VolumeVolume measures how much a solid can measures how much a solid can “hold”.“hold”.

Count Up the VolumeCount Up the Volume1.1. Find the volume of the Find the volume of the

right rectangular prism.right rectangular prism.

2.2. Write a formula for Write a formula for finding the volume of a finding the volume of a right rectangular prism.right rectangular prism.

3.3. What is the area of a What is the area of a rectangle?rectangle?

4.4. How does the shape of How does the shape of the base work into the the base work into the volume formula?volume formula?

lw

H

V = l · w · H

Find the VolumeFind the Volume

1.1. Ask: What is the Ask: What is the shape of the base?shape of the base?

2.2. V = l w HV = l w H

3.3. V = (8)(3.6)(4.5)V = (8)(3.6)(4.5)

8 in

4.5 in

3.6 in

129.6 in3

Find the VolumeFind the Volume1.1. What is the shape What is the shape

of the base?of the base?

2.2. V = ½ b h HV = ½ b h H

3.3. V = ½ (43)(68)V = ½ (43)(68)(29)(29)

V = 42,398 mmV = 42,398 mm33

29 mm

68 mm 43 mm

Cavalieri’s PrincipleCavalieri’s Principle

Turn to page 626 in your book.Turn to page 626 in your book.

Cavalieri’s principle states that if two prisms Cavalieri’s principle states that if two prisms have the same base area and the same have the same base area and the same height, then they will have the same height, then they will have the same volume. volume.

That means whether you have a right prism That means whether you have a right prism or an oblique prism, the volume will be the or an oblique prism, the volume will be the same.same.

TheoremTheorem

The volume of a right rectangular The volume of a right rectangular prism is the product of its length, prism is the product of its length, width, and height.width, and height.

V = l w HV = l w H

lw

H

TheoremTheorem

The volume of any prism is the product of The volume of any prism is the product of the area of its base and its height.the area of its base and its height.

V = b HV = b H

We will be working with prisms with We will be working with prisms with square, rectangular and triangular square, rectangular and triangular bases.bases.

Ask: What is the shape of the base?Ask: What is the shape of the base?

Assignment 9-2AAssignment 9-2APage 628, 11-12, 27-28Page 628, 11-12, 27-28

and worksheetand worksheet

NO FORMULAS WITH NUMBERS

NO CREDIT