1. Surface Area and Volume
Scale factor
Surface Area and Volume

2. Scale factor
Scale factor is a number that you multiply a measurement by to increase or decrease in size.

3. Scale factor
A scale factor is used to scale shapes in 1, 2, or 3 dimensions.
Scale factor can be found in the following scenarios:
Size Transformation: In size transformation, the scale factor is the ratio of expressing the amount of magnification.
Scale Drawing: In scale drawing, the scale factor is the ratio of measurement of the drawing compared to the measurement of the original figure.
Comparing Two Similar Geometric Figures: The scale factor when comparing two similar geometric figures, is the ratio of lengths of the corresponding sides.

4. Scale factor calculation
3 times bigger
Scale
Image
3cm
Actual
9cm
9cm
Scale factor =
Ratio would be
9 = 3
Can be written as a decimal 3.0 as a percentage =300% or as a ratio 3:1

5. If decimal value is more than one it is an enlargement
If decimal value is less than one it is a reduction

6. Applying Scale Factor Applying a scale factor of 3:5 to rectangle
Would the scaled image be an enlargement or a reduction
Reduction
What would the dimensions be of the new image.
To find dimensions multiply each of the dimensions with the scale factor
7.4cm
2.2cm
3:5 = 3/5 = 0.6
Less than 1 so this is a reduction
To calculate the dimensions of the scaled image multiply the dimensions of the actual image with the scale factor.
2.2 (0.6) = '22 6
1.32
7.4(0.6) = 74
4.44
To determine the original size of an object the dimension of scaled image is divided by scale factor.

7. Ratio of area Find the ratio of the lengths of sides
Square the ratio to find the ratio of the surface areas e f d
2cm b c a
5cm
Ratio of the lengths is 5:2
5²:2² = 25:4
1:4/25 = Dividing each number by 25

8. How surface area and volume are affected by scale factor
4cm A
2cm B
Find the ratio of the LENGTHS of sides
SQUARE the ratio to find the ratio of the surface areas
CUBE the ratio of lengths to find the ratio of the volume.
4/2 = 2/1
2/1 x 2/1 = 4/1
2/1 x 2/1 x 2/1 = 8/1
Summary
Side lengths = 2 times longer for A
Surface area = 4 times larger for A
Volume = 8 times larger for A

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