Finding mass of black hole once given the density

AI Thread Summary
To calculate the mass of a black hole with a given density of 750 kg/m^3, the Schwarzschild radius formula is utilized, which relates mass and density. The equation D = (mass/(4/3π((2Gmass/c^2)^3)) presents challenges in isolating the mass due to its complexity. The key step involves correctly applying the exponent to all components within the brackets. By simplifying the algebra, it becomes feasible to solve for mass. This method allows for determining the mass based on the specified density.
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Homework Statement


Calculate the mass and radius of a black hole with density 750 kg/m^3.

Homework Equations


The Attempt at a Solution


In a previous question, I already used the Schwarzschild radius to come up with a formula for the density of a black hole:
D = (mass/(4/3pi((2Gmass/c^2)^3). I realize that this should be enough to solve for mass, but I am having difficulty with the algebra...How do I solve for mass when one of the "mass" variables is stuck inside the Scharzchild radius in a complicated fraction?
 
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Apply the ^3 to everything inside the brackets to which it is attached.
 

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