- #1
Darragh
- 1
- 0
Hi gang, I was given this question, but I can't quite seem to get it all the way...
1.Determine the coordinates of the centroid of the surface of a
hemisphere, the radius of which is r, with respect to its base.
A=2[itex]\pi r^{2}[/itex]
A: Surface Area of the Hemisphere.
Coordinates of the centroid: ([itex]\overline{X}, \overline{Y}, \overline{Z}[/itex])
[itex]\overline{Y}A = \int ydA[/itex]
I set up the coordinate system so [itex]\overline{X}[/itex] = 0 and [itex]\overline{Z}[/itex] = 0
I tried finding the circular elements of the hemisphere
r[itex]_{el}[/itex]=[itex]\sqrt{r^{2}-y^{2}}[/itex]
r[itex]_{el}[/itex]: Radius of the element
dA=2[itex]\pi\sqrt{r^{2}-y^{2}}[/itex]dy
Then I used [itex]\overline{Y}( 2\pi r^2) = \int^{r}_{0} y 2 \pi \sqrt{r^2-y^2} dy[/itex]
but I'm pretty sure this is wrong, any ideas or pointers? Thanks in advance.
1.Determine the coordinates of the centroid of the surface of a
hemisphere, the radius of which is r, with respect to its base.
Homework Equations
A=2[itex]\pi r^{2}[/itex]
A: Surface Area of the Hemisphere.
Coordinates of the centroid: ([itex]\overline{X}, \overline{Y}, \overline{Z}[/itex])
[itex]\overline{Y}A = \int ydA[/itex]
I set up the coordinate system so [itex]\overline{X}[/itex] = 0 and [itex]\overline{Z}[/itex] = 0
The Attempt at a Solution
I tried finding the circular elements of the hemisphere
r[itex]_{el}[/itex]=[itex]\sqrt{r^{2}-y^{2}}[/itex]
r[itex]_{el}[/itex]: Radius of the element
dA=2[itex]\pi\sqrt{r^{2}-y^{2}}[/itex]dy
Then I used [itex]\overline{Y}( 2\pi r^2) = \int^{r}_{0} y 2 \pi \sqrt{r^2-y^2} dy[/itex]
but I'm pretty sure this is wrong, any ideas or pointers? Thanks in advance.