两球的体积之和是12pai,它们的大圆周长之和是6pai,则两球的半径之差的绝对值是
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/22 00:47:01
![两球的体积之和是12pai,它们的大圆周长之和是6pai,则两球的半径之差的绝对值是](/uploads/image/z/3935611-19-1.jpg?t=%E4%B8%A4%E7%90%83%E7%9A%84%E4%BD%93%E7%A7%AF%E4%B9%8B%E5%92%8C%E6%98%AF12pai%2C%E5%AE%83%E4%BB%AC%E7%9A%84%E5%A4%A7%E5%9C%86%E5%91%A8%E9%95%BF%E4%B9%8B%E5%92%8C%E6%98%AF6pai%2C%E5%88%99%E4%B8%A4%E7%90%83%E7%9A%84%E5%8D%8A%E5%BE%84%E4%B9%8B%E5%B7%AE%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%E6%98%AF)
两球的体积之和是12pai,它们的大圆周长之和是6pai,则两球的半径之差的绝对值是
两球的体积之和是12pai,它们的大圆周长之和是6pai,则两球的半径之差的绝对值是
两球的体积之和是12pai,它们的大圆周长之和是6pai,则两球的半径之差的绝对值是
设两球半径分别为R和r,则:
(4/3)π(R^3+r^3)=12π
2π(R+r)=6π
即:
R^3+r^3=(R+r)(R^2-Rr+r^2)=9 R+r=3
R^2-Rr+r^2=3 R=3-r
(3-r)^2-(3-r)r+r^2=3
r^2-3r+2=0
R=2 r=1
R-r=1