1. Drill
Solve for x:
Find the surface Area of a rectangular prism if the dimensions are 3 x 5 x 6.
Find the volume of a right cylinder with radius 5 cm. and height 6 cm.

2. 10.5 & 10.6 Perimeter, Area and Volume Ratios

3. Exploration #1
Find the ratio of the sides in two squares if the sides in one square are 3 units and the sides in the other square are 1 unit.
What are the areas of those same two squares? Find the ratio of the areas of the same two squares.
Ratio is 3/1
Ratio is 9/1

4. What is the ratio of sides in two rectangles where the dimensions of the two rectangles are 9 x 18 and 6 x 12 respectively?
What is the ratio of the areas of the same two rectangles?
Ratio is 3/2
Ratio is 9/4

5. What is the ratio of radii in two circles whose radii are 8 and 6 respectively?
What is the ratio of the areas in those same two circles?
Ratio is 4/3
Ratio is 16/9

6. What is the relationship?
The ratio of the areas is just the ratio of the sides (radii) squared.
Example: If the ratio of the sides is 2:3, then the ratio of the areas is 4:9

7. Exploration # 2 Find the volume of the objects on the worksheets.
Try and come up with a rule for the relationship between the ratio of the sides and the ratio of the volumes.
The ratio of volumes is equal to the cubes of the ratio of the sides.

8. Ratio of Sides
Ratio of Perimeters
Ratio of Areas
Ratio of Volumes
1 : 2
2 : 3
5 : 7
1 : 81
9 : 25
125: 216
1 : 2
1 : 4
1 : 8
2 : 3
4 : 9
8 : 27
5 : 7
25 : 49
125 : 343
1 : 9
1 : 9
1 : 729
3 : 5
3 : 5
27 : 125
5 : 6
5 : 6
25 : 36

9. Homework
Finish Worksheet