Question

Circle R was dilated to form circle R'. The diameter of circle R is 7 units and the diameter of circle R' is 28 units. What is the relationship between the areas of circle R and circle R'?

1.The area of circle R' would be 1/4 of the original area.
2.The area of circle R' would be 16 times the original area.
3.The area of circle R' would be 1/16 of the original area.
4.The area of circle R' would be 4 times the original area.

Answer 1

The area of circle R' would be 16 times the original area of circle R.

Step-by-step explanation:

The relationship between the areas of circle R and circle R' can be determined by comparing their radii. The ratio of the radii is equal to the ratio of the areas.

Given that the diameter of circle R is 7 units and the diameter of circle R' is 28 units, the radius of circle R is 3.5 units (half of the diameter) and the radius of circle R' is 14 units. Therefore, the ratio of the radii is 14/3.5 = 4.

The area of a circle is proportional to the square of its radius. So, if the ratio of the radii is 4, the ratio of the areas will be 4^2 = 16.

Therefore, the correct relationship between the areas of circle R and circle R' is that the area of circle R' would be 16 times the original area of circle R.