04/26/11
Changing Dimensions
LT: I will describe how increasing or decreasing a measurement will
affect area and volume.
Warm-Up
Find the volume and surface area to the nearest
tenth.
V= 4,069.4 m3
SA=1582.6 m2
Today’s Plan:
-Warm up
-Changing Dimensions
-Assignment
LT: I will describe how increasing or
decreasing a measurement will affect
area and volume.
04/26/11
Changing Dimensions
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?
Today’s Plan:
-Warm up
-Changing Dimensions
-Assignment
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.
7 in
3 in
5 in
The original box has a volume of (5)(3)(7) = 105 cm3.
V = (15)(3)(7) = 315 cm3
Tripling the length would
triple the volume.
Try This: Example 2A
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.
The original box has a volume of (5)(3)(7) = 105 cm3.
V = (5)(3)(21) = 315 cm3
Tripling the height would
triple the volume.
Try This: Example 2A
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.
The original box has a volume of (5)(3)(7) = 105 cm3.
V = (5)(9)(7) = 315 cm3
Tripling the width would
triple the volume.
Try This: Example 2A
A box measures 5 in. by 3 in. by 7 in. Explain
what tripling the length, width, and height of
the box will do.
The original box has a volume of (5)(3)(7) = 105 cm3.
V = (15)(9)(21) = 2835 cm3
Tripling the length, width,
and height would make the
volume 27 times bigger!
04/26/11
Changing Dimensions
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?
Today’s Plan:
-Warm up
-Changing Dimensions
-Assignment
LT: I will describe how increasing or
decreasing a measurement will affect
area and volume.
Try This: Example 2B
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.
The original cylinder has a volume of 4 • 3 = 12 cm3.
V = 4 • 9 = 36 cm3
Tripling the height would
triple the volume.
Try This: Example 2B
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.
The original cylinder has a volume of 4 • 3 = 12 cm3.
V = 36 • 3 = 108 cm3
By tripling the radius,
you would increase the
volume nine times.
Additional Example 2B: Exploring the Effects of
Changing Dimensions
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.
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
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?
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.
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 2
A 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.
Original Dimensions
V=
=
1
3
1
3
r2h
(22)5
 20.93 m3
Double the Height
V=
=
1
3
1
3
r2
(2h)
(22)(2•5)
 41.87 m3
Double the Radius
V=
=
1
3
1
3
 (2r)2h
(2 • 2)2(5)
 83.73 m3
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 2
Find the volume of each figure to the
nearest tenth.Use 3.14 for .
3. Explain whether tripling the height of a
square pyramid would triple the volume.
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.
04/26/11
Changing Dimensions
LT: I will describe how increasing or decreasing a measurement will
affect area and volume.
What about Surface Area?
Predict:
What affect will tripling the radius or height have
on the surface area of a cylinder?
Today’s Plan:
-Warm up
-Changing Dimensions
-Assignment
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 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
LT: I will describe how increasing or decreasing a measurement will
affect area and volume.
Assignment: pg 494 #1-3,5-7,9
Today’s Plan:
-Warm up
-Changing Dimensions
-Assignment
LT: I will describe how increasing or
decreasing a measurement will affect
area and volume.