How Do You Solve These Challenging Calculus Problems?

[Kobrakai]

I am having trouble with these two problems, I was wondering if anyone here could help me.

1. Given a sphere of radius 10 inches. Calculate the altitude of the inscribed right circular cylinder of maximum volume.

2. A man 6 feet tall walks away from a light 30 feet high at the rate of 3 miles per hour. How fast is the further end of his shadow moving, and how fast is his shadow lengthening?

 

[Euclid]

Here's where to started with number 1:
If the height of the cylinder is h, what is its radius (in terms of h)? What is its volume?

 

[Galileo]

For 2:
Introduce an angular variable \theta which is the angle between the line connecting the mans head and the light source and the vertical.
Express how theta changes with the mans velocity and get the length of the shadow as a function of theta.

 

[mathwonk]

i think my post pointing out the key relations needed to sove the rpoblem, i.e. pythagoras and simialr triangles repsectively, contain the most difficult part of the solution for most students. were they omitted because i gave my information too efficiently?, i.e. in one sentence?

 

[Galileo]

i think my post pointing out the key relations needed to sove the rpoblem, i.e. pythagoras and simialr triangles repsectively, contain the most difficult part of the solution for most students. were they omitted because i gave my information too efficiently?, i.e. in one sentence?

Nothing's been omitted, but this exact same question has been posted in General Math too.

 

[mathwonk]

thanks. i am confused by all the repeat questions.