Apc.3.1.8 difference in sphere volume

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SUMMARY

The discussion centers on calculating the difference in volume between two spheres with radii 3.1 and 3 using the formula for the volume of a sphere, \( V = \dfrac{4}{3}\pi r^{3} \). Participants emphasize the importance of calculus, specifically the derivative \( \dfrac{dV}{dr} \), to find the linear approximation of the volume change. The conversation highlights the need for a solid understanding of differential calculus to accurately approach this problem.

PREREQUISITES
  • Understanding of sphere volume formula \( V = \dfrac{4}{3}\pi r^{3} \)
  • Basic knowledge of calculus, particularly derivatives
  • Familiarity with linear approximation techniques
  • Concept of differential calculus
NEXT STEPS
  • Study the concept of derivatives in calculus
  • Learn about linear approximation methods in mathematical analysis
  • Explore the application of differential calculus in geometry
  • Review examples of volume calculations for different geometric shapes
USEFUL FOR

Students and educators in mathematics, particularly those focusing on calculus and geometry, as well as anyone interested in understanding volume changes in three-dimensional shapes.

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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