I am doing some analysis of results from an impact crater caused by steel balls. I am measuring the diameter of the impact crater and need to link it to the volume of the crater using the volume of resolution. Can anybody help I have a formula that I derived it is correct?

 

Volume of moved by impact = (2/3) π r3 – (1/12) π(4r2-D2)3/2

where r is the radius of the steel ball and D is the diameter of the crater.

This i think is linking the diameter of impact crater to the volume moved...

 

I also have two other calculus problems:

I need to find out the surface area of the crater in terms of the diameter of the impact crater can anybody help???

 

Then I need the rate of change of surface area with respect to diameter and then to depth???

 

These problems are beyond my mathematical skills...

don't you also need the depth of the crater to work out its volume?

As (diameter of crater/2)^2 = (radius of the steel ball)^2 + Radius of steelball - depth of crater)^2

 

which is just the equation of a circle.

 

There is a definite relationship so that if you know diameter of the crater you also know the depth.