- #1

- 1

- 0

**1.Determine the coordinates of the centroid of the surface of a**

hemisphere, the radius of which is r, with respect to its base.

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.