Question

半径为R的圆铁片剪去一扇形做圆锥,问留下的扇形的中心角α多大时圆锥的容积最大?

Answer 1

设圆锥底面半径r 圆锥高h

r=a*r/2л

h^2=R^2-r^2=...=R/2л*√(4л^2-a^2)

v=л*r^2*h/3=[a^2*R^3√(4л^2-a^2)]/24л^2

v^2=(1/2)*(a^3/24л^2)*a^2*a^2(8л-2a^2)