



 
Terry, In my diagram C is the center of the sphere, R is its radius so in your situation R = 2 m, h is the height of the cone and r is the radius of the base of the cone. All the dimensions are in meters. The volume of a cone is V = 1/3 π r^{2} h and this is what you want to maximize. The task as usual with this type of problem is to write V a a function of one variable alone so you need an expression relating r and h so that you can eliminate one of them. I would use the right triangle ABC. Pythagoras theorem will give you an expression that allows you to substitute for r^{2} in the expression for the volume and leave you with an expression for h alone since you know the value of R. Apply the calculus you know to maximize V. Harley  


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