Archimedes Principle: Calculate Outer & Inner Radii

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To solve for the outer radius of a spherical aluminum ball with a mass of 1.48 kg that barely floats in water, the effective density of the ball must be nearly equal to that of water. The buoyant force, calculated using the density of water and the volume of the ball, should equal the mass of the ball. The volume of the ball can be expressed in terms of its outer radius, while the volume of the cavity will be based on its inner radius. By equating the mass of the ball to the buoyant force, both the outer radius and the radius of the cavity can be determined. This approach utilizes Archimedes' principle to find the necessary dimensions.
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Homework Statement


A spherical aluminum ball of mass 1.48 kg contains an empty spherical cavity that is concentric with the ball. The ball just barely floats in water.
A. Calculate the outer radius of the ball.

B. Calculate the radius of the cavity


Homework Equations


Buoyant Force = density of fluid * Volume of object *g


The Attempt at a Solution

 
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If the ball barely floats in water, then it's effective density must be vey nearly equal to water. So, equate the mass of the ball to the buoyant force. Also, vol of water = vol of the ball.
 
You'll need the density of Al.
 
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