MHB Apc.3.1.8 difference in sphere volume

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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
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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.
 
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