Related Rates: Circles and Changing Circumference

Click For Summary

Homework Help Overview

The problem involves related rates concerning the circumference and diameter of a circle, specifically examining how the diameter changes over time as the circumference increases at a given rate.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the rate of change of circumference and diameter, questioning the relevance of the radius in the context of the problem. Some express uncertainty about whether the provided information about the radius is necessary for solving the problem.

Discussion Status

There appears to be a consensus among some participants regarding the irrelevance of the radius in this specific context, with guidance offered on the relationship between the rates of change of circumference and diameter.

Contextual Notes

Participants are operating under the assumption that the rate of change of circumference is a constant, and there is a focus on understanding the implications of this relationship without resolving the initial question completely.

Qube
Gold Member
Messages
461
Reaction score
1

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.
 
Physics news on Phys.org
Hi Qube! :smile:
Qube said:
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! :biggrin:
 
  • Like
Likes   Reactions: 1 person
Qube said:

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.
 
Mark44 said:
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!
 

Similar threads

Find the derivative of a balloon's circumference
  • · Replies 4 ·
Replies
4
Views
2K
How Fast is the Radius of a Circle Increasing When a Stone is Dropped in Water?
  • · Replies 3 ·
Replies
3
Views
3K
Related rates problem for the dimensions of a cylinder
  • · Replies 11 ·
Replies
11
Views
2K
Simple circle problem involving area and circumference
  • · Replies 34 ·
2
Replies
34
Views
4K
Related rates & unknown factors
  • · Replies 3 ·
Replies
3
Views
2K
Rate of change of area in sphereical baloon, .
  • · Replies 8 ·
Replies
8
Views
2K
Spherical balloon related rates problem
  • · Replies 10 ·
Replies
10
Views
6K
Rates of change: surface area and volume of a sphere
  • · Replies 3 ·
Replies
3
Views
5K
Rates of change: inflated hot-air balloon
  • · Replies 3 ·
Replies
3
Views
2K
A different related rates problem - no time mentioned
  • · Replies 13 ·
Replies
13
Views
2K