# Density of a floating sphere

1. Nov 28, 2014

### throneoo

1. The problem statement, all variables and given/known data
a sphere of uniform density and radius R is floating on water , partially immersed such that the distance between the top of the sphere and the water surface is R/2
find the density of the sphere
2. Relevant equations
Archimedes Principle

3. The attempt at a solution
One can deduce from the Archimedes Principle ,that the weight of the displaced water = the weight of the object

ρWaterVDisplaced waterg=ρObject VObjectg

which basically turns the problem into a mathematical problem involving finding the volume of the immersed part of the sphere.

Consider a circle of radius R centered at the origin ,

the required volume is ∫π(R2-x2)dx from -R to R/2 = 9πR3/8

Thus , ρObject=(9πR3/8)/(4πR3/3) * ρWater

=27/32 ρWater

I dunno if it's a legitimate method . It is suggested that I utilize the concept of hydrostatic pressure instead , but i have no idea how to do that.[/SUB]

2. Nov 28, 2014

### ehild

It is legitimate and correct. The buoyant force is equal to the weight of the displaced fluid.