Related Rates: Circles and Changing Circumference

[Qube]

Homework Statement

The circumference of a circle is increasing by 4 inches per second. What is the rate of change of the diameter with respect to time if the radius is 2 inches?

Homework Equations

C = 2∏r = ∏d.

The Attempt at a Solution

dC/dt = 4 = ∏dd/dt.

dd/dt = 4/∏

Is this it? It seems as if the information given about the radius is irrelevant.

 

[tiny-tim]

Hi Qube!

The circumference of a circle is increasing by 4 inches per second. What is the rate of change of the diameter with respect to time if the radius is 2 inches?
…
It seems as if the information given about the radius is irrelevant.

yup!

 

[Mark44]

Homework Statement

The circumference of a circle is increasing by 4 inches per second. What is the rate of change of the diameter with respect to time if the radius is 2 inches?

Homework Equations

C = 2∏r = ∏d.

The Attempt at a Solution

dC/dt = 4 = ∏dd/dt.

dd/dt = 4/∏

Is this it? It seems as if the information given about the radius is irrelevant.

Yes, this is it. The circumference is a constant multiple of the diameter, so the rates of change of circumference and diameter are also going to be constant multiples of one another.

 

[Qube]

Yes, this is it. The circumference is a constant multiple of the diameter, so the rates of change of circumference and diameter are also going to be constant multiples of one another.

Alright, thanks guys. Thanks for the explanation; this provides an easy way to check!