The area of circle B is 16 times greater than the area of circle A. Which of the following statements is true? A. The circumference of circle B is 16 times greater than the circumference of circle A. B. The circumference of circle A is 16 times greater than the circumference of circle B. C. The circumference of circle B is 4 times greater than the circumference of circle A. D. The circumference of circle A is 4 times greater than the circumference of circle B.

Remark

The general formula for the area of a circle is Area = pi r^2

The general formula for the circumfrerence of a circle = 2 * pi * r

Discussion

You could work with numbers to indicate what the answer might be. You are not asked to prove anything - - just indicate it. Suppose r = 2 for the small circle. It's area is

A = pi (2) ^2

A = 4*pi

Now you want the second circle to be 16 times as big

16 * 4*pi = pi r1^2 divide both sides by pi

16*4 = r1^2

r1^2 = 64

r1 = 8

Conclusion

Radius Circle A = 2

Radius Circle B = 8

Solution

A

Circumference A = 2 * pi * r = 2 * pi * 2 = 4*pi

Circumference B = 2 * pi * r1 = 2 * pi * 8 = 16 pi

Ratio B/A = 16 pi / 4pi = 4

A is false. It is only 4 times larger.

B

The relationship of A to B in circumference is 4 not 16. Answer B is wrong. A and B answers are both wrong.

C

The correct answer is C. B is 4 times greater than A.

D

D is wrong A is 1/4 the size of B.

I took the test and got C) Correct