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 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? Original Problem P = 2(7) + 2(4) P = 14 + 8 P = 22 Proportional Change P = 2(7 x 2) + 2(4 x 2) P = 2(14) + 2(8) P = 28 + 16 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.

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 ½ Twice 2 Doubled Tripled 3 Quadrupled 4

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) 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) 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.

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.

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 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. 1536 ÷ 24 = 64 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? (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.

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

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

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)

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)

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!!