Question

/已知球的半径为R.球内接圆柱的底面半径为r.高为h.则r和h为何值时,内接圆柱最大

Answer 1

已知球的半径为R

V（柱）=πr^2*h h/2=√R^2-r^2

V(柱）=2πr^2√R^2-r^2

=2π√R^2r^4-r^6

V’=2π*（4R^2r^3-6r^5)/2√R^2r^4-r^6=0

3r^2=2R^2 r=√6R/3 h=2√3R/3

内接圆柱最大.