Exploration similarity

1. Choose a number between 2 and 10. This is the length of a line segment. If you dilate the line segment by a factor of 3, what is the relationship between the lengths of the line segment and its dilation?
2. Choose another number between 2 and 10. This is the length of a side of a square. If you dilate the square by a factor of 4, what is the relationship between the area of the square and its dilation?
3. Choose another number between 2 and 10. This is the length of one side of a cube. If you dilate the cube by a factor of 2, what is the relationship between the volume of the cube and its dilation? What if the cube were a sphere? Or a pyramid? Does the relationship of the volumes change?
4. Television sets used to come with an aspect ratio of 4:3 (width is 4 units and height is 3 units). Since broadcast channels in the United States are now broadcasting in 16:9, most newer sets come with a 16:9 aspect ratio. Since we can rewrite the ratio 16:9 as , does that mean we could define a 4:3 television set as being similar to a  television set? Why or why not?

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