Question

The diameter of a circular chip is doubled to use in a new board game, The area of the new chip will be _____.twice as large as the area of the old chipeight times as large as the area of the old chipfour times as large as the area of the old chipone-half as large as the area of the old chip

Answer 1

If any 2D shape is scaled in such a way that the length of one of its parts is scaled by a factor k, then its area will be scaled by a factor k².

For example, if a square with side length equal to 1 is scaled by a factor of 3, its sides will now have a measure of 3 but its area will have a measure of 9, which is 3²:

Then, if the diameter of a circular chip is scaled up by a factor of 2, its area will be scaled up by a factor 2², which is equal to 4:

Therefore, if the diameter is doubled, the area of the new chip will be four times as large as the area of the old chip.