Question

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ing Rectangles a rectangle with an area of 20cm2 magine a ould its length and width be? List at least five different combinations. enlarging each of your rectangles by a scale factor of 2: 2n List the dimensions of your enlarged rectangles and work out their areas. What do you notice? Try starting with rectangles with a different area and enlarge them by a scale factor of 2. What happens now? Can you explain what's going on? What happens to the area of a rectangle if you enlarge it by a scale factor of 3? Or 4? Or 5? What happens to the area of a rectangle if you enlarge it by a fractional scale factor? What happens to the area of a rectangle if you enlarge it by a scale factor of k? Explain and justify any conclusions you come to Do they apply to plane shapes other than rectangles? Now explore what happens to the surface area and volume of different cuboids when they are enlarged by different scale factors. Explain and justify any conclusions you come to Do your conclusions apply to solids other than cuboids rce: From

Answer 1

Area of 20 sq. cm

Its dimensions could by 1 x 20 or 2 x 10 or 4 x 5 etc

Scaling by factor of 2, we get 2 x 40, 4 x 20, 8 x 10 as the new dimensions

Areas of each of these is 80 sq. cm

Suppose we started with area of 15 sq. cm

Dimensions could be 1 x 15, 3 x 5 etc

Scaling by factor of 2, we get 2 x 30, 6 x 10 etc

Areas of each of these is 60 sq. cm

In each of these cases, area has increased by a factor of 4

Suppose we scaled by factor of 3

Dimensions would be 3 x 45, 9 x 15 etc

Areas are 135 sq. units

Area has increased by factor of 9

Scaling by factor of 4, area increases by factor of 16

Scaling by factor of 5, area increased by factor of 25

In general, scaling by factor of k, area increases by factor of k² (for a planar shape)

This applies to all shapes in a plane (2D shape)

For a 3-D cuboid whose volume is 120

Its dimensions could be 3 x 4 x 10, 4 x 5 x 6, 3 x 5 x 8

Scaling by factor of 2, dimensions become

6 x 8 x 20, 8 x 10 x 12, 6 x 10 x 16

Whose volumes are not 960 cubic units

Volume is 8 times original volume now

In general, after scaling by factor of k volume will be k³ times original volume