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

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Presentation transcript:

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

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

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

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

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

Formula A = l w w Original Problem w A = 7(4) w A = 28 w Proportional Change w A = (7 doubled )(4 doubled ) w A = (7 2)(4 2) w A = (14)(8) w 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 7 by 4

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

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

Formula V = l w h w Original Problem w V = 4(2)(3) w V = 24 w Proportional Change w V = (4 4)(2 4)(3 4) w V = (16)(8) (12) w 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 4 by 2 by 3

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

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

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

Geometry formula method w How would the area change if the dimensions of the rectangle are 5 times the original size? Pick “baby numbers” A = 6 A = times bigger

Effect of Change Formula w 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 w What would the new perimeter be if the dimensions are quadrupled? 3 ft. 4 ft.

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

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