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.
