Question

【急】在平面直角坐标系中,△ABC的两个顶点A与B在x轴上运动,且AB=2,顶点C的坐标C(0,根号2）

Answer 1

不妨设A在B的左边,设A(a,0),则B(a+2,0)

当a≥0时,

旋转体的体积=COB旋转所得圆锥体积-COA旋转所得圆锥体积

=2πOC^2XOB/3-2πOC^2XOA/3

=(2/3)πOC^2X(OB-OA)

=(2/3)πOC^2XBA

=(8/3)π

当-2＜a≤0时,

旋转体的体积=COB旋转所得圆锥体积+COA旋转所得圆锥体积

=2πOC^2XOB/3+2πOC^2X|OA|/3

=(2/3)πOC^2X(OB+|OA|)

=(2/3)πOC^2X|BA|

=(8/3)π

当a≤-2时,

旋转体的体积=COA旋转所得圆锥体积-COB旋转所得圆锥体积

=2πOC^2X|OA|/3-2πOC^2X|OB|/3

=(2/3)πOC^2X(|OA|-|OB|)

=(2/3)πOC^2X|BA|

=(8/3)π

没有变化.