Question

设Ω={（x，y，z）|x2+y2≤z≤1}，则Ω的形心的竖坐标.z=2323．

设Ω={（x，y，z）|x2+y2≤z≤1}，则Ω的形心的竖坐标.z=2323．

Answer 1

∵Ω的体积V＝

?

Ω

dxdydz
=

∫

1 0

dz

?

x2+y2≤z

dxdy
=

∫

1 0

πzdz=

π

2

∴

.

z

＝

? Ω zρdxdydz

M

＝

1

V

?

Ω

zdxdydz
=

∫

1 0

zdz

?

x2+y2≤z

dxdy
=

1

V

∫

1 0

πz2dz
=

1

V

?

π

3

=

2

3