Rate of change of area of circle in respect to radius

In summary, the rate of change of the area of a circle with respect to the radius is equal to the circumference of the circle. The formula for circumference is 2(pi)r and the units for rate of change are given as (pi)in^2/in. This is because we are representing the rate of change, so it is better to use units that reflect this.
  • #1
grace77
43
0
What is the Rate of change of area of circle in respect to radius when radius is 3in
I know that that dA/dr is equal to the circumference of the circle
But where does that come from?
Also the formula for the circumference of the circle is 2(pi)r
But the answer is 6 (pi)in^2/in.
I understand the 6 but where are the units coming from if the circumference of the circle will only give you units for r ?

Hope someone can shed some light on this for me! Thanks
 
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  • #2
It is rate of change of AREA wrt RADIUS. What are the units of these two?
 
  • #3
PhysicoRaj said:
It is rate of change of AREA wrt RADIUS. What are the units of these two?
Ok so you basically use the formula for the circumference of the circle but use the units for area/radius?
 
  • #4
Both are one and the same. But since we are representing the rate of change, it is better to use units like that.
 
  • #5
PhysicoRaj said:
Both are one and the same. But since we are representing the rate of change, it is better to use units like that.
Thank you.
 
  • #6
Homework questions need to be posted in the homework forums.
 

What is the formula for the rate of change of area of a circle in respect to its radius?

The formula for the rate of change of area of a circle in respect to its radius is given by dA/dr = 2πr, where dA/dr represents the rate of change and r represents the radius of the circle.

How do you interpret the rate of change of the area of a circle in respect to its radius?

The rate of change of the area of a circle in respect to its radius represents the slope of the graph of the circle's area with respect to its radius. This means that for every unit increase in the radius, the area of the circle will increase by a rate of 2π.

Does the rate of change of the area of a circle increase or decrease as the radius increases?

The rate of change of the area of a circle increases as the radius increases. This is because as the radius increases, the circle's area increases at a faster rate due to the fact that the circumference increases as well.

Can the rate of change of the area of a circle ever be negative?

No, the rate of change of the area of a circle cannot be negative. This is because as the radius increases, the area of the circle will always increase, even if the rate of change decreases. Therefore, the rate of change will always be positive or zero.

How is the rate of change of the area of a circle related to its circumference?

The rate of change of the area of a circle is directly proportional to its circumference. This means that as the circumference increases, the rate of change of the area also increases. This can be seen in the formula, where the rate of change is represented by 2π, the same value used in the formula for the circumference of a circle.

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