1. 8.4 Volume and Areas of Similar Figures
Geometry
Topic/Objective: To find the volume and surface area of similar figures.
EQ: How do you find the surface area and volume of similar figures?

2. 8.4 volume and Areas of Similar Figures
Is this statement True or False?
The picture is twice as big as our smaller TV.
Screen Size: 6  9
Screen Size: 12  18
Area: 54
Area: 216
8.4 volume and Areas of Similar Figures

3. 8.4 volume and Areas of Similar Figures
Problem
Draw a rectangle that measures 3  2. 6
The area is ?
Double the lengths of the sides and draw a rectangle that measures 6  4.
The area is ? 24
8.4 volume and Areas of Similar Figures

4. 8.4 volume and Areas of Similar Figures
Example continued
When the lengths of the sides were doubled, did the area double?
NO! 6 24
8.4 volume and Areas of Similar Figures

5. 8.4 volume and Areas of Similar Figures
So what happened? 3
The ratio of the sides: 6 2 ?
The ratio of the areas: 6 ? 24 4
8.4 volume and Areas of Similar Figures

6. 8.4 volume and Areas of Similar Figures
Notice: 3
The ratio of the sides: 6 2
The ratio of the areas: 6 24 4
8.4 volume and Areas of Similar Figures

7. 8.4 volume and Areas of Similar Figures
Example 2
These figures are similar. The area of the smaller one is 20. Find the area of the larger figure. 4
Ratio of the sides:
Ratio of their areas: 10
8.4 volume and Areas of Similar Figures

8. 8.4 volume and Areas of Similar Figures
Example 2 continued
Write the proportion and solve: 20
125 x 4 10
Ratio of sides 2:5
Ratio of areas 4:25
8.4 volume and Areas of Similar Figures

9. 8.4 volume and Areas of Similar Figures
Problem
If the figures are similar, what is the length of the side marked x? 4
A = 36 x
A = 100
Remember: the ratio of the areas is the square of the ratios of the sides.
Or, the ratio of the sides is the square root of the ratios of the areas.
8.4 volume and Areas of Similar Figures

10. 8.4 volume and Areas of Similar Figures
Problem Solution 4
A = 36 x
A = 100
The ratio of the sides is the square root of the ratios of the areas.
8.4 volume and Areas of Similar Figures

11. 8.4 volume and Areas of Similar Figures
Volume and Surface area of similar solids.
8.4 volume and Areas of Similar Figures

12. 8.4 volume and Areas of Similar Figures
The ratio of sides cubed gives us the ratio of volume.
Side length is doubled: Scale factor is 2
tells us the scale factor of volume.
8.4 volume and Areas of Similar Figures

13. 8.4 volume and Areas of Similar Figures
Summary:
The scale factor of all areas of similar figures and solids is the scale factor of sides squared.
The scale factor of all volumes of similar solids is the scale factor of sides cubed.
8.4 volume and Areas of Similar Figures