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

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.

Formula P = 2 • l + 2 • w How do the perimeters change? 7 by 4 Formula P = 2 • l + 2 • w Original Problem P = 2(7) + 2(4) P = 14 + 8 P = 22 Proportional Change P = 2(7 doubled) + 2(4 doubled) P = 2(14) + 2(8) P = 28 + 16 P = 44 How do the perimeters change? Divide the new perimeter by the original perimeter. When the dimensions doubled, the perimeter doubled

Solve the same problem using the effect of change formula How would the perimeter change if the dimensions of the rectangle are doubled? (dimension change) PAV# 7 ft. (2) 1 = 2 4 ft. The new perimeter will be double the original perimeter

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.

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

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

Volume of a rectangular prism How would the volume change if the dimensions are quadrupled? 3 ft. 2 ft. 4 ft.

Formula V = l • w • h How do the volumes change? Original Problem 4 by 2 by 3 Formula V = l • w • h Original Problem V = 4(2)(3) V = 24 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. When the dimensions quadrupled, the volume increased by 64 times the size of the original

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

What to do if NO dimensions are given Do the math...pick “baby numbers” to compute if no numbers are given. Apply scale factor change. Divide. Use the Effect of change formula (scale factor) PAV#

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

Geometry formula method How would the area change if the dimensions of the rectangle are 5 times the original size? Pick “baby numbers” 3 A = 150 10 2 A = 6 25 times bigger 15

Effect of Change Formula How would the area change if the dimensions of the rectangle are 5 times the original size? (scale factor) PAV# (5) 2 = 25 times bigger

Volume of a rectangular prism What would the new perimeter be if the dimensions are quadrupled? 4 ft. 3 ft.

Volume of a rectangular prism What would the new area be if the dimensions are tripled? 4 ft. 6 ft.

Volume of a rectangular prism What would the new volume be if the dimensions are doubled? 4 ft. 3 ft. 6 ft.