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Effect of Change

Effect of Change. The effects on perimeter, area, and volume when dimensions are changed proportionally. 14 ft. 8 ft. Perimeter of a Rectangle. How would the perimeter change if the dimensions of the rectangle are doubled ?. 7 ft. 4 ft. Original Problem P = 2(7) + 2(4) P = 14 + 8

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Effect of Change

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

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

  3. 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 Formula P = 2 • l + 2 • w 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.

  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) 1 = 2 4 ft. The new perimeter will be double the original perimeter.

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

  7. Original Problem A = 7(4) A = 28 Proportional Change A = (7 • 2)(4 • 2) A = (14)(8) A = 112 Formula A = l • w 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. Original Problem V = 4(2)(3) V = 24 Proportional Change V = (4 • 4)(2 • 4)(3 • 4) V = (16)(8) (12) V = 1536 Formula V = l • w • h 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.

  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 areachange if the dimensions of the rectangle are 5 timesthe original size? (Change in Dimension) PAVExponent (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) PAVExponent (4) 1 = 4 times bigger 4 ft. 3 ft. Old Perimeter = 14 x 4= 56 (New Perimeter)

  15. Area of a Rectangle • What would the new area be if the dimensions are tripled? (Change in Dimension) PAVExponent (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) PAVExponent 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!!

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