When my son comes home from school needing help with this . . .
A cylinder with height 2x is inscribed in a sphere with radius 10.
a) Show that the volume of the cylinder, V, is 2πx(100 – x2).
b) By using calculus, one can show that V is maximum when x = 10√3 divided by 3. Substitute this value for x to find the maximum volume V. max. V = 4000π√3 divided by 9.
c) Use a calculator or computer to evaluate V= 2πx(100-x2) for various values of x between 0 and 10. Show that the maximum volume V occurs when x ≈ 5.77.
…boy am I glad I married my husband.
And what’s really sad is that I couldn’t even type the problem and had to get my son to do it for me…I mean, when was the last time you typed a square root, an exponent, or the symbol for pi? Hmmm?