Final answer:
A black hole would need to be extremely massive to have the density of water, with its mass being determined by the relationship between event horizon radius and density. However, such a black hole would be an unrealistic scenario due to the way black holes form and behave in our universe.
Step-by-step explanation:
The student has asked how massive a black hole would have to be to have the density of water. To explore this, we must first understand the nature of black holes and how their density is determined by their mass and the radius of their event horizon. The density ρ of a spherical object is given by the formula ρ = Mass/Volume. In the case of a black hole, the volume is derived from the volume of a sphere V = 4/3πr³, where r is the radius of the event horizon.
The density of water is approximately 10³ kg/m³. To find a black hole with this density, we would set the black hole's mass over its volume equal to the density of water and solve for the mass M. As the radius r of a black hole's event horizon is directly proportional to its mass (r = 2GM/c², where G is the gravitational constant and c is the speed of light), this results in a black hole mass that is so large that its density equals that of water. However, due to the immense mass required and the way black holes are understood scientifically, such a black hole would not be feasible