1. Effect of Change
The effects on perimeter, area, and volume when dimensions are changed proportionally.

2. Perimeter of a Rectangle
How would the perimeter change if the dimensions of the rectangle are doubled?
14 ft.
8 ft.
7 ft.
4 ft.

3. Formula P = 2 • l + 2 • w How do the perimeters change?
Original Problem
P = 2(7) + 2(4)
P =
P = 22
Proportional Change
P = 2(7 x 2) + 2(4 x 2)
P = 2(14) + 2(8)
P =
P = 44
How do the perimeters change?
Divide the new perimeter by the original perimeter. 44 ÷ 22 = 2. When the dimensions doubled, the perimeter doubled.

4. We can solve the same problem using the effect of change formula
Formula: (change in dimension)PAV Exponent
Common Changes in Dimension:
PAV Exponent : The number you put as an exponent when solving a Perimeter (1), Area (2), or Volume (3) problem.
Changes in Dimensions
# for Formula
Halved
Twice 2
Doubled
Tripled 3
Quadrupled 4

5. Solve the same problem using the effect of change formula
How would the perimeter change if the dimensions of the rectangle are doubled?
(change in dimension) PAV Exponent
7 ft.
(2) = 2
4 ft.
The new perimeter will be double the original perimeter.

6. Area of a Rectangle
How would the area change if the dimensions of the rectangle are doubled?
14 ft.
8 ft.
7 ft.
4 ft.

7. Formula A = l • w How do the areas change? Original Problem A = 7(4)
Proportional Change
A = (7 • 2)(4 • 2)
A = (14)(8)
A = 112
How do the areas change?
Divide the new area by the original area. 112 ÷ 28 = 4. When the dimensions doubled the area increased by 4 times the original size.

8. Solve the same problem using the effect of change formula
How would the area change if the dimensions of the rectangle are doubled?
(Change in Dimension) PAV Exponent
7 ft.
(2) 2 = 2 x 2 = 4
4 ft.
The new area will be 4 times the original area.

9. Volume of a Rectangular Prism
How would the volume change if the dimensions are quadrupled?
3 ft.
2 ft.
4 ft.

10. Formula V = l • w • h How do the volumes change? Original Problem
Proportional Change
V = (4 • 4)(2 • 4)(3 • 4)
V = (16)(8) (12)
V = 1536
How do the volumes change?
Divide the new volume by the original volume ÷ 24 = 64
When the dimensions quadrupled, the volume increased by 64 times the size of the original.

11. Solve the same problem using the effect of change formula
How would the volume change if the dimensions of the shape are quadrupled?
(Change in Dimension) PAV Exponent
3 ft.
(4) 3 = 4 x 4 x 4 = 64
2 ft.
The new volume will be 64 times the original volume.
4 ft.

12. Perimeter of a Rectangle
How would the area change if the dimensions of the rectangle are 5 times the original size?

13. Effect of Change Formula
How would the area change if the dimensions of the rectangle are 5 times the original size?
(Change in Dimension) PAV Exponent
(5) 2 = 5 x 5 = 25 times bigger

14. Perimeter of a Rectangle
What would the new perimeter be if the dimensions are quadrupled?
(Change in Dimension) PAV Exponent
(4) 1 = 4 times bigger
4 ft.
3 ft.
Old Perimeter = 14 x 4= 56 (New Perimeter)

15. Area of a Rectangle (Change in Dimension) PAV Exponent
What would the new area be if the dimensions are tripled?
(Change in Dimension) PAV Exponent
(3) 2 = 3 x 3 = 9 times bigger
4 ft.
6 ft.
Old Area = 24 x 9= 216 (New Area)

16. Volume of a rectangular prism
What would the new volume be if the dimensions are doubled?
(Change in Dimension) PAV Exponent
4 ft.
(2) 3 = 2 x 2 x 2 = 8 times bigger
3 ft.
6 ft.
Old Volume= 72 x 8= 576 (New Volume)
THANK YOU AND HAVE A GREAT DAY!!