Volume of a cube versus side length

Click For Summary

Homework Help Overview

The discussion revolves around the relationship between the volume of a cube and its edge length, specifically focusing on the rate of change of volume with respect to edge length and its connection to surface area.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the derivative of the volume function and its relation to the surface area, with initial attempts to establish the mathematical connection between these quantities.

Discussion Status

Some participants have identified the derivative of the volume as a key aspect of the discussion, noting that it relates to the surface area. There is acknowledgment of the relationship without a definitive conclusion on the overall implications.

Contextual Notes

Participants are working within the framework of calculus, specifically derivatives, and are discussing the properties of geometric shapes without additional context or constraints.

emma3001
Messages
41
Reaction score
0
Show that the rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of a cube.

I know that surface area= 6l^2(because of the six faces)
I know that volume is l^3. How do I relate volume then to edge length
 
Physics news on Phys.org
emma3001 said:
Show that the rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of a cube.


The "rate of change" is the derivative.

So what is the derivative of the volume with respect to the edge length?
 
Thanks! I now realize that the first derivative of the volume is 3l^2, which is half the surface area
 
Right.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
9
Views
1K
  • · Replies 33 ·
2
Replies
33
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
Replies
10
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 16 ·
Replies
16
Views
2K