Question

(pi为圆周率)两个球体体积之和为12pi且两球大圆周厂之和为6pi求两球半径之差?

Answer 1

设两球半径X,Y (4/3)pi*X^3+(4/3)pi*Y^3=12pi X^3+Y^3=9 (X+Y)(X^2-XY+Y^2)=9 (X+Y)((X+Y)^2-3XY)=9------------------(1) 而:2pi*X+2pi*Y=6pi X+Y=3,代入(1),得:3(9-3XY)=9 XY=2 (X-Y)^2=(X+Y)^2-4XY=3^2-4*2=1 两球半径之差=|X-Y|=1