# Chapter 16 - A Macroscopic Description of Matter - Exercises and Problems - Page 464: 2

The density of the nucleus is $2.3\times 10^{17}~kg/m^3$

#### Work Step by Step

We can find the volume of the nucleus as: $V = \frac{4}{3}\pi~R^3$ $V = \frac{4}{3}\pi~(7.5\times 10^{-15}~m)^3$ $V = 1.767\times 10^{-42}~m^3$ We can find the density of the nucleus as: $\rho = \frac{m}{V}$ $\rho = \frac{4.0\times 10^{-25}~kg}{1.767\times 10^{-42}~m^3}$ $\rho = 2.3\times 10^{17}~kg/m^3$ Thus, the density of the nucleus is $2.3\times 10^{17}~kg/m^3$.

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