Perimeter , Area and Volume with changed dimensions
Given a rectangle with dimensions of 6 by 4.
Perimeter: ______
Area: ______
Double the dimensions of the rectangle (multiply each side by 2)
New Perimeter: ______
New Area: ______
Compare the effects on the perimeter and area when dimensions of a shape are changed (dilated) proportionally. Complete the chart below:
Smaller Larger Ratio of larger Rectangle Rectangle dimension to smaller dimension Length Width Perimeter Area
Conclusion: Perimeter , Area and Volume with changed dimensions
If the dimensions of the rectangle are doubled (scale factor of 2): the perimeter is______
If the dimensions of the rectangles are doubled (scale factor of 2): the area is ______
Extension:
If the dimensions of the rectangle are tripled (scale factor of 3): the perimeter is ______
If the dimensions of the rectangle are triples (scale factor of 3): the area is ______
What do you think will happen to volume when dimensions are changed proportionally?
Given a rectangular prism with dimensions of 6 by 4 by 2:
Volume: ______
Double the dimensions of the prism:
New Volume: ______
Perimeter , Area and Volume with changed dimensions
Smaller Rectangle Larger Rectangle Ratio of larger dimension to smaller dimension Length Width Height Volume
Since each dimension was dilated (multiplied) by 2, then the volume was multiplied by 8: or 23 (scale factor cubed) Why do you think the volume is “cubed”?
Perimeter , Area and Volume with changed dimensions
Effects on perimeter, area and volume when dimensions of a shape are changed proportionally:
Original Scale factor Perimeter Area Volume times 2 times 2=___ times 22=___ times 23=___
times 3
times 4
1 times 2
2 times 3
3 times 4
Examples:
1. Find the surface area of a prism whose dimensions are triple those of a prism with surface area 94 cm2.
2. Find the volume of a cylinder whose dimensions are double those of a cylinder with volume 110 cm3.
1 3. Perimeter of a triangle is 24 ft. The dimensions are dilated by a scale factor of What 4. is the new perimeter?
4. Area of a triangle is 420 square inches. The dimensions are dilated by ½ . What is the area of the new triangle?
5. The volume of a cube is 40 cubic feet. If the dimensions are doubled, what is the volume of the new cube?
Perimeter , Area and Volume with changed dimensions
Original Scale factor Perimeter Area Volume From 8 in³ to 64 in³
From 27 in³ to 729 in³
From 125 in³ to 8 in³
From 216 in³ to 27 in³
From 25 in² to 16 in²
From 4 in² to 36 in²
From 121 in² to 49 in²
From 81 in² to 144 in²
From 25 in to 16 in
From 25 in to 100 in
From 10.5 m to 0.9 m
From 20 ½ m to 45 ¼ m
Perimeter , Area and Volume with changed dimensions