在高为H,底面半径为R的圆锤内作一内接圆柱体,则圆柱体的底面半径r为多大时

设内接圆柱体半径r,高h.则有r/R=(H-h)/H,变化得：h=(1-r/R)H(1)圆柱体体积V=πr^2h=πr^2(1-r/R)H=-πHr^3/R+πHr^2=V(r)求导有V'(r)=-3πHr^2/R+2πHr=-πHr(3r/R-2),当V'(r)=0时取得极大值,此时3r/R-2=0,得：r=2R/...