04/26/11 Changing Dimensions

Today’s Plan:-Warm up -Changing Dimensions-Assignment

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

Warm-UpFind the volume and surface area to the nearest tenth.

V= 4,069.4 m3

SA=1582.6 m2

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

04/26/11 Changing Dimensions

Today’s Plan:-Warm up -Changing Dimensions-Assignment

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

Predict:

What affect will tripling the length, width, or height have on the volume of a rectangular prism?

What if the length, width, AND height were tripled?

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box.

Tripling the length would triple the volume.

V = (15)(3)(7) = 315 cm3

The original box has a volume of (5)(3)(7) = 105 cm3.5 in

3 in

7 in

A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box.

Try This: Example 2A

The original box has a volume of (5)(3)(7) = 105 cm3.

Tripling the height would triple the volume.

V = (5)(3)(21) = 315 cm3

A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box.

Try This: Example 2A

Tripling the width would triple the volume.

V = (5)(9)(7) = 315 cm3

The original box has a volume of (5)(3)(7) = 105 cm3.

A box measures 5 in. by 3 in. by 7 in. Explain what tripling the length, width, and height of the box will do.

Try This: Example 2A

Tripling the length, width, and height would make the volume 27 times bigger!

V = (15)(9)(21) = 2835 cm3

The original box has a volume of (5)(3)(7) = 105 cm3.

04/26/11 Changing Dimensions

Today’s Plan:-Warm up -Changing Dimensions-Assignment

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

Predict:

What affect will tripling the radius or height have on the volume of a cylinder?

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume.

Try This: Example 2B

Tripling the height would triple the volume.

V = 4 • 9 = 36 cm3

The original cylinder has a volume of 4 • 3 = 12 cm3.

By tripling the radius, you would increase the volume nine times.

A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume.

Try This: Example 2B

V = 36 • 3 = 108 cm3

The original cylinder has a volume of 4 • 3 = 12 cm3.

A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius.

Additional Example 2B: Exploring the Effects of Changing Dimensions

By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

02/25/10 Changing Dimensions #16

Today’s Plan:-Warm up and Correct Homework-Changing Dimensions-Assignment

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

Predict:

What affect will tripling the radius or height have on the volume of a cone?

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

Additional Example 2: Exploring the Effects of Changing Dimensions

A cone has a radius of 3 ft. and a height of 4 ft. Explain whether tripling the height would have the same effect on the volume of the cone as tripling the radius.

When the height of the cone is tripled, the volume is tripled. When the radius is tripled, the volume becomes 9 times the original volume.

Try This: Example 2A cone has a radius of 2 m and a height of 5 m. Explain whether doubling the height would have the same effect on the volume of the cone as doubling the radius.

Double the RadiusDouble the HeightOriginal Dimensions

13

V = r2h13

13

13= (22)5

20.93 m3

13

V = r2 (2h)

= (22)(2•5) = (2 • 2)2(5)

V = (2r)2h

41.87 m3 83.73 m3

13

When the height of a cone is doubled, the volume is doubled. When the radius is doubled the volume is 4 times the original volume.

Lesson Quiz: Part 2Find the volume of each figure to the nearest tenth.Use 3.14 for .

Yes; the volume is one-third the product of the base area and the height. So if you triple the height, the product would be tripled.

3. Explain whether tripling the height of a square pyramid would triple the volume.

04/26/11 Changing Dimensions

Today’s Plan:-Warm up -Changing Dimensions-Assignment

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

Predict:

What affect will tripling the radius or height have on the surface area of a cylinder?

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

What about Surface Area?

Additional Example 2: Exploring the Effects of Changing Dimensions

A cylinder has diameter 8 in. and height 3 in. Explain whether tripling the height would have the same effect on the surface area as tripling the radius.

They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height.

04/26/11 Changing Dimensions

Today’s Plan:-Warm up-Changing Dimensions-Assignment

LT: I will describe how increasing or decreasing a measurement will affect area and volume.

Assignment: pg 494 #1-3,5-7,9

LT: I will describe how increasing or decreasing a measurement will affect area and volume.