Question

已知球的半径为R,球的内接圆柱的底面半径为r,高为h,则r和h为何值时,内接圆柱的体积最大?

Answer 1

(2r)^2+h^2=(2R)^2

4r^2+h^2=4R^2

V=πr^2h

V^2=(π^2)(r^4)(h^2)

=[(π^2)/4]*(2r^2)(2r^2)(h^2)