Perform the following calculation: \[ \left(7.85 \times 10^{9}\right) \div\left[(4 / 3) \times 3.1416 \times\left(2.53 \times 10^{4} \mathrm{~cm}\right)^{3}\right] \] Answer: $\mathrm{g} / \mathrm{cm}^{3}$

Step 1 ：The problem is asking for the density of a substance, given its mass and volume. The mass is given as \(7.85 \times 10^{9}\) g and the volume is given as the volume of a sphere with radius \(2.53 \times 10^{4}\) cm.

Step 2 ：The formula for the volume of a sphere is \(\frac{4}{3} \pi r^{3}\), where \(r\) is the radius of the sphere.

Step 3 ：We can calculate the volume using this formula: \[\left(\frac{4}{3} \times 3.1416 \times \left(2.53 \times 10^{4}\right)^{3}\right)\] which gives us a volume of approximately \(67834428871197.5\) cm\(^3\).

Step 4 ：We then divide the mass by the volume to get the density: \[\left(7.85 \times 10^{9}\right) \div \left(\frac{4}{3} \times 3.1416 \times \left(2.53 \times 10^{4}\right)^{3}\right)\]

Step 5 ：This gives us a density of approximately \(0.00011572294674884645\) g/cm\(^3\).

Step 6 ：Final Answer: The density of the substance is approximately \(\boxed{0.00011572294674884645}\) g/cm\(^3\).