MHB Inverse variation or direct or neither?

  • Thread starter Thread starter woof123
  • Start date Start date
  • Tags Tags
    Inverse Variation
Click For Summary
The volume of a sphere, represented by the formula V=(4/3)pi*r^3, demonstrates a direct variation with the cube of the radius, r^3. While some may initially perceive it as direct variation with r, it is important to clarify that V does not vary directly with r itself. Instead, the relationship is defined by the constant factor (4/3)pi, indicating that volume increases with the cube of the radius. Therefore, the correct interpretation is that the volume varies directly with r^3, not r. Understanding this distinction is crucial in mathematical discussions of variation.
woof123
Messages
9
Reaction score
0
the volume of a sphere: V=(4/3)pi*r3

To me it looks like it is direct variation with a power function (V/r3=(4/3)*pi)but i don't think that's what they're looking for
 
Mathematics news on Phys.org
Strictly speaking, neither, as $V$ does not vary directly with $r$.

It does, however, vary directly with $r^3$, as $\dfrac{4}{3}\pi$ is a constant.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Calculating the inverse of a function involving the error function
  • · Replies 3 ·
Replies
3
Views
2K
High School Are Inverse Problems More Complex Than Direct Problems in Mathematics?
  • · Replies 13 ·
Replies
13
Views
3K
Graduate Margules' Power Series Formula: Deriving Coefficients
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What are the applications of inverses of vector functions?
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad Calculus of Variations on Kullback-Liebler Divergence
  • · Replies 3 ·
Replies
3
Views
2K
High School A question about one of Archimedes' works
  • · Replies 5 ·
Replies
5
Views
2K
High School How to calculate the gain or loss percentage in short sell?
  • · Replies 5 ·
Replies
5
Views
5K
MHB Vertical and Horizontal Asymptotes
  • · Replies 3 ·
Replies
3
Views
2K
Electromagnetism problem: Merging of 2 charged drops of mercury
  • · Replies 2 ·
Replies
2
Views
1K
MHB Approximation of eigenvalue with inverse iteration method
  • · Replies 2 ·
Replies
2
Views
1K