THINK LINE Imagine a line wrapped around the figure. Units are cm. ft. in. etc. 2 2 Perimeter is ONE...

THINK LINE

Imagine a line wrapped around the figure. Units are cm. ft. in. etc.2

2

Perimeter is ONE DIMENSION

DIMENSIONAL

What is the Perimeter of the square?

THINK SQUARES

How many squares would it take to cover the inside of a figure?Units are cm2 ft2 in2 etc.

Area has TWO DIMENSIONS.

DIMENSIONAL

What is the Area of the figure?

THINK CUBES

How many cubes would it take to build it or to fill it?

Units are cm3 ft3 in3 etc.

Volume has THREE DIMENSIONS.

DIMENSIONAL

What is the Volume of the figure?

THINK SQUARES

How many squares would it take to cover the inside of a figure?Units are cm2 ft2 in2 etc.

THINK LINE

Imagine a line wrapped around the figure. Units are cm. ft. in. etc.2

2

THINK CUBES

How many cubes would it take to build it or to fill it?Units are cm3 ft3 in3 etc.

We were to increase each dimension by a scale factor of 2? In other words, we would double the dimensions or multiply by 2.

If the WAS 8

You could take 8 (the original perimeter) x the scale factor (2) 8 x 2 = 16 so the NEW PERIMETER IS 16.

2

22

2

4

4

4

4

You could double each side andRe-calculate the perimeter…..OR

We were to increase each dimension by a scale factor of 2? In other words, we would double the dimensions or multiply by 2.

If the WAS 14

4

3

You could double each side andRe-calculate the perimeter…..OR

8

6

You could take 14 (the original perimeter) x the scale factor (2) 14 x 2 = 28 so the NEW PERIMETER IS 28.

We were to increase each dimension by a scale factor of 2? In other words, we would double the dimensions or multiply by 2.

If the WAS 4

You could double each side andRe-calculate the area…..OR

You could take 4 (the original area) x the scale factor (2) squared. 4 x 22 = 16 so the NEW AREA IS 16. Since area involves 2 dimensions we must use scale factor to the power of 2 (squared)!

We were to increase each dimension by a scale factor of 2? In other words, we would double the dimensions or multiply by 2.

If the WAS 12

You could double each side andRe-calculate the area…..OR

You could take 12 (the original area) x the scale factor (2) squared. 12 x 22 = 48 so the NEW AREA IS 48. Since area involves 2 dimensions we must use scale factor to the power of 2 (squared)!

4

3

And we were to increase each dimension by a scale factor of 2? In other words, we would double the dimensions or multiply by 2.

the

WAS 8

You could double each dimension (remember with volume there are 3) andRe-calculate the volume…..OR

2

2

2

You could take 8 (the original volume) x the scale factor (2) cubed. 8 x 23 = 64 so the NEW volume IS 64. Since volume involves 3 dimensions we must use scale factor to the power of 3 (cubed)!

4

4

4

the

WAS 24

4

3

2

and we were to increase each dimension by a scale factor of 2? In other words, we would double the dimensions or multiply by 2.

You could… double each dimension (remember with volume there are 3) andRe-calculate the volume…..OR

You could take 24 (the original volume) x the scale factor (2) cubed. 24 x 23 = 192 so the NEW volume IS 192. Since volume involves 3 dimensions we must use scale factor to the power of 3 (cubed)!

8

6

4

We were to increase each dimension by a scale factor of 3 ? Or a scale factor of 4? Or a scale factor of 5 ???

Original perimeter x scale factor

Original area x scale factor squared

Original Volume x scale factor cubed

What if we increase each dimension by a scale factor of 3 ? Or a scale factor of 4? Or a scale factor of 5 ???

Perimeter x scale factor Area x scale factor squared Volume x scale factor cubed

Original perimeter = 6 Original area = 6 Original volume = 6

6 x 3

6 x 4

6 x 5

6 x 32

6 x 42

6 x 52

6 x 33

6 x 43

6 x 53

x 3x

If the volume of the smaller cube is 9, what would be the volume of the larger cube?

Is multiplying 9 times 3 enough???

Remember, Volume involves 3 dimensions, so you have to use the scale factor of 3 to the power of 3 (33).

Volume = 9

Volume = ? Find your answer before going on to the next slide.

x 3x

Volume = 9

Volume = 243

Original volume 9 x 33 scale factor cubed

9 x (3x3x3) 9 x 27 243

Find your answer before going on to the next slide.

3

2

If you double the dimensions of the smaller rectangle, what would be the area of the larger rectangle?

Would taking 6 x 2 be enough? How many dimensions are we affecting when looking at area? Remember area deals with 2 dimensions so you must take the scale factor to the power of 2.

Area = 6

3

2

Area = 6

Original area 6 x 22 scale factor squared

6 x (2 x 2) 6 x 4 24

Area = 24

5

3

Perimeter = Area =

The larger rectangle was created using a scale factor of 2.5. Find the perimeter and area of the smaller rectangle and then give the perimeter & area of the larger rectangle.

Find your answer before going on to the next slide.

5

3

Perimeter = 16 unitsArea = 15 units2

Perimeter 16 x 2.5 = 40Original perimeter x scale factor

Area 16 x 2.52 16 x 6.25100 square units

Original area x scale factor2

Perimeter x scale factor Area x scale factor squared Volume x scale factor cubed

There are 6 questions that follow. Show your work on paper. Number each item and turn it in. Refer back to the examples if you need to. THINK!!! Draw pictures!!

What will be the area of an enlargement if each dimension is multiplied by 4?

6

4

1.

16

4

Suppose the rectangle above is reduced by cutting each dimension in half. What would be the perimeter of the reduction?

2.

16

4

Suppose the rectangle above is reduced by cutting each dimension in half. What would be the area of the reduction?

3.

The volume of the box above is 125 cm3 . Find the volume of a similar box if each dimension were doubled.

55

54.

If the perimeter of the larger square is 16, What would be the the perimeter of the smaller square?

x12 x

5.

If the height and the circumference of the larger cylinder is twice that of the smaller one, what would be the volume of the larger cylinder?

Volume = 120 ft3

Volume = ?

6.