Solutions to Lesson 8 Packet

Investigation 1:

1. 10, 40, 4/1, 2/1 -- notice that 4/1 is the square of 2/1

2. 12, 108, 12/108 = 1/9, 8/24 = 1/3 -- notice that 1/9 is the square of 1/3

3. 4Pi, 9Pi, 4/9, 2/3 -- notice that 4/9 is the square of 2/3

Proportional Area Rule: If two similar figures have corresponding lengths in a ratio of m/n, then their AREAS are in a ratio of (m/n) squared!

Investigation 2:

1. 2/5, 8/25

2. 3/4, 27/64

3. 1/2, 1/8

4. 6/9, 216/729

Notice in each case above -- the ratio of volumes is equal to the ratio of the lengths CUBED!

Proportional Volume Rule: If two similar figures have corresponding lengths in a ratio of m/n, then their VOLUMES are in a ratio of (m/n) cubed!

Practice:

1. 18

2. 18

3. a = 5, b = 10

4. 27Pi

5. 1:49

6. 1:3

7. (m/n)^3

8. ratios of volumes: 27/729, ratio of areas: 9/81

9. Annie should charge the client $6,000 since doubling the lengths means the area will increase by 4 times. So charge 4 times the original price of $1500.

10. 12.8 oz of dough.

11. Volume of large Pyramid: 1,715 cubic cm

12. h = 4, H = 16, Ratio of Volumes = 1/64

Solutions to Lesson 8 HW Packet - FRONT

1. Ratio of Perimeters: 4:5, Ratio of Areas: 16/25

2. Ratio of Perimeters: 3:5, Ratio of Areas: 9/25

3. Ratio of Perimeters: 3:4, Ratio of Areas: 9/16

4. Approx. 2.8/5.7

5. 9/5

6. Approx. 3.16/18.97

7. Square root 128Pi / Square root of 18Pi

8. 48

9. 180

10. 28.8

11. Square root of 12/27

12. 1/2

13. Square root of 8/50

Solutions to Lesson 8 HW Packet - FRONT

1. 1:9, 1:27

2. 25:4, 125, 8

3. 5:6, 125:216

4. 2/3, 8/27

5. 1/3, 1/9

6. 4/3, 16/9

7. 54Pi

8. 40

9. 600

10. 21.6Pi

11. 54,000 lbs.

12. 5 lbs

13. 16 lbs.

14. .0017 lbs.