A ring has a inner circumference of 9 centimeters.If the ring's inner circumference can vary between 8 centimeters and 10 centimeters how can the radius vary? Round your answer to
Five decimal places.
A)Radius can vary between 6.48456 centimeters and 10.13212 centimeters.
B)Radius can vary between 1.59577 centimeters and 1.78412 centimeters.
C)Radius can vary between 1.27324 centimeters and 1.59155 centimeters.
D)Radius can vary between 2.54648 centimeters and 3.18310 centimeters.
E)Radius can vary between 0.43239 centimeter and 2.43239 centimeters.

Question

Quizplus · Accepted Answer

The inner circumference of a ring is given by the formula:

C = 2πr

where C is the circumference and r is the radius.

We are given that the inner circumference of the ring is 9 cm. So we can write:

9 = 2πr

Solving for r, we get:

r = 9/(2π) ≈ 1.43239 cm

Now, the inner circumference can vary between 8 cm and 10 cm. So we need to find the range of values for r that correspond to these circumference values.

When the inner circumference is 8 cm, we have:

8 = 2πr

Solving for r, we get:

r = 4/π ≈ 1.27324 cm

When the inner circumference is 10 cm, we have:

10 = 2πr

Solving for r, we get:

r = 5/π ≈ 1.59155 cm

So the radius can vary between 1.27324 cm and 1.59155 cm. Therefore, the best answer choice is C. We know that the inner circumference of the ring (C) is given by $C = 2\pi r$, where $r$ is the radius. 
So, $C = 2\pi r = 9 \implies r = \frac{9}{2\pi} \approx 1.43239$ cm. 
Now, we need to find the range of values for $r$ when the circumference varies between 8 cm and 10 cm. 
When $C = 8$, we have $r = \frac{4}{\pi} \approx 1.27324$ cm. 
When $C = 10$, we have $r = \frac{5}{\pi} \approx 1.59155$ cm. 
Therefore, the radius can vary between 1.27324 cm and 1.59155 cm.

A Ring Has a Inner Circumference of 9 Centimeters