Instantaneous rate of change of a sphere

AI Thread Summary
To find the instantaneous rate of change of the volume V of a sphere with respect to its radius r, the derivative of the volume formula V=4/3π(r^3) must be calculated. The derivative is dV/dr = 4πr^2. Evaluating this at r=5 micrometers gives a non-zero result, specifically 100π micrometers squared. The initial confusion stemmed from misunderstanding the nature of the derivative, which is not zero. Understanding the correct application of calculus is crucial for solving such problems.
ivysmerlin
Messages
2
Reaction score
0

Homework Statement


Find the instantaneous rate of change of V with respect to r when r=5 micrometers


Homework Equations



V=4/3pi(r^3)

The Attempt at a Solution



would you just take the derivative? and if so, wouldn't it just be zero, because it comes out to be a real number, right? but that doesn't seem right...
 
Physics news on Phys.org
What is the derivative of V=4/3pi(r^3)? Now what would the value be at r=5micrometers? Not zero.
 
ooh, I am an idiot, thanks
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Estimated Instantaneous Rate Of Change
Replies
2
Views
6K
Precalculus -- determine the rate of change of the function
Replies
3
Views
1K
I Limits confusion -- What is meant by "instantaneous rate of change"?
Replies
18
Views
2K
Why is current defined as the rate of change of charge?
Replies
6
Views
2K
Complex Roots of Z^n = a + bi: Finding Solutions Using De Moivre's Theorem
Replies
18
Views
2K
Comparing V and SA of a torus vs sphere
Replies
4
Views
3K
How Retirement Changes Affect Unemployment Rates
Replies
4
Views
3K
What Is the Yearly Growth Rate for a 40% Increase Over Three Years?
Replies
8
Views
2K
Instantaneous and Average Rate of Change of f(x) | Interval (0,3)
Replies
3
Views
2K
Calculating Instantaneous Rate of Change for a Quadratic Function
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top