# Homework Help: Buoyant Force acting on a sphere

1. Dec 10, 2015

### Carrie

1. The problem statement, all variables and given/known data
A sphere of radius 10.0 cm floats in equilibrium partially submerged in water with its lowest point 5.00 cm below the water's surface.

(a) What is the buoyant force acting on the sphere?

2. Relevant equations
F = pvg

3. The attempt at a solution
F= 1000 * v * 9.8

V= 4/3*pi*(r)^3 and then I multiplied this by 1/2 because half of it is submerged.

F= 1000 * 1/2(4/3*pi*(.1)^3) * 9.8
F= 202 N, but the answer is 6.42 N, so that is very wrong.

Thank you!!!!

2. Dec 10, 2015

### SteamKing

Staff Emeritus

3. Dec 10, 2015

### Carrie

I think I might have messed up putting it in my calculator, because now I'm getting 20.5 N.

4. Dec 10, 2015

### Staff: Mentor

The sphere's radius is 10 cm. The lowest point is 5 cm below the water's surface. Sketch it.

5. Dec 10, 2015

### SteamKing

Staff Emeritus
Closer, but still not what I calculated.

6. Dec 10, 2015

### Carrie

Okay, I sketched it and now I'm wondering if I use half that radius of 10 cm because it's half submerged. So:

F= 1000 * 1/2(4/3*pi*(.05)^3) * 9.8 = 5.13 N. I'm not sure if I'm going off in the wrong direction now.

7. Dec 10, 2015

### SteamKing

Staff Emeritus
No, the sketch is very helpful here. You want to find the volume of part of a sphere, what is called a spherical cap, like this (the blue region would be submerged):

https://en.wikipedia.org/wiki/Spherical_cap

I think I misread the problem like you did in my initial attempt at calculation, so the book answer could be correct.

8. Dec 10, 2015

### Carrie

Oh, that makes sense! Thank you for your help!