MHB Apc.3.1.8 difference in sphere volume

Click For Summary
The discussion focuses on calculating the difference in volume between two spheres with radii 3 and 3.1 using the formula for the volume of a sphere. Participants suggest using linear approximation and calculus concepts, specifically the derivative of volume with respect to radius. There is a clarification that a partial derivative is not needed for this calculation. The conversation emphasizes the importance of understanding the underlying calculus principles to solve the problem effectively. Understanding these concepts is crucial for accurate volume calculations in geometry.
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
?
 
Last edited:
Physics news on Phys.org

Terrible question. Maybe the best LINEAR approximation? Or words to that effect.

$$\dfrac{4}{3}\pi(3.1)^3-\dfrac{4}{3}\pi (3)^3$$

Are you studying geometry or calculus? You don't seem to have used any calculus.

Please read up on "differential". You'll need some sort of partial derivative.
 
it was originally from barrons but couldn't find it

Ill delete it
 
Why not learn from it.

Start with $$V = \dfrac{4}{3}\pi r^{3}$$

Calculate $$\dfrac{dV}{dr}$$

Okay, so it's not a "partial" derivative.
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
View full post »

Similar threads

High School Question about volume of a sphere
  • · Replies 16 ·
Replies
16
Views
3K
MHB -apc.4.1.2 Find the slope at x=4
  • · Replies 7 ·
Replies
7
Views
2K
MHB *15.4.17 Volume between a cone and a sphere
  • · Replies 2 ·
Replies
2
Views
9K
MHB APC.5.2.01 AP Volume by Rotation
  • · Replies 8 ·
Replies
8
Views
1K
MHB -apc.2.1.06 crosses the x-axis at one point in the interval [0,1]
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Volume of sphere using integration?
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad Calculating the change of the volume of a sphere using this integral
  • · Replies 3 ·
Replies
3
Views
3K
Change in volume of sphere with change in temperature
  • · Replies 19 ·
Replies
19
Views
2K
Undergrad Deriving the volume of a sphere using semi-circles
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Volume element in Spherical Coordinates
  • · Replies 5 ·
Replies
5
Views
4K