Calculating Depth of Immersion of an Ice Cone in Water

[cooney88]

1. an ice cone 25mm high with a max radius of 15mm is floating apex downwards in a glass of water. if the ice cone has a mass of 5.3g to what depth will the cone be immersed? density of water is 1000kg/m^3



i know from the law of flotation that the weight of a floating body is equal to the weight of the fluid it displaces

so i should be using bouyancy = s1 x w / s

s1= density of object s = relative density of fluid and w is the wieght of the object but i can't seem to link this equation with anoter to find the depth.

maybe x/l x W?

The Attempt at a Solution

 

[LowlyPion]

You know the mass of the water that needs to be displaced.

Now the question arises what % of the volume of the cone will it immerse.

You might approach it as what is the size of a cone of displaced water that's equal to the mass of the original cone. Then that should tell you the depth of the ice cone that will be submerged shouldn't it? (You will need to keep the radius and the height in the same ratio.)