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# Calculus/Vol and Area

Question
Hi Scotto,

The Volume of a sphere is 4/3 pi r^3 and the area is the first differential ie 4pir^2. Since the first differential of a slope is a straight line why then is the first differential of volume=area. How about if I take the first differential of the area ie 8*pi*r..does it mean anything? Thanks!

If the equation gives the volume, the derivative of this usually gives the surface area.
For a sphere, 4πr³/3.  The derivative, 4π², is the surface area.  I'm not sure what the next derivative is used for in volume.

As far as distance, the distance fallen due to gravity (in meters) is 9.81t²/2.
The derivative is this with respect to time t is 9.81t, and that is the velocity.
the derivative of velocity is 9.81, and that is the acceleration.

Falling from rest, after 2 second has passed, the distance is 9.81*2²/2 = 19.62.
The velocity is 9.81*2 = 19.62.  The second derivative, 9.81, is the acceleration.
This means acceleration is always the same.  That is, of course, neglecting wind resistance.

Calculus

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#### Scotto

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