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**1. Homework Statement**

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. Homework 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

ρ

_{Water}V

_{Displaced water}g=ρ

_{Object}V

_{Object}g

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(R

^{2}-x

^{2})dx from -R to R/2 = 9πR

^{3}/8

Thus , ρ

_{Object}=(9πR

^{3}/8)/(4πR

^{3}/3) * ρ

_{Water}

=27/32 ρ

_{Water}

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]