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.

15.5

step-by-step explanation:

5

∑

n = 1

substitute n = 1, 2, 3, 4, 5 and sum the terms

= + + + 2² + 2³

= 0.5 + 1 + 2 + 4 + 8

= 15.5

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6