2009

The mean density of a supermassive black hole

Round: Theory
Points: 10
Level: Bronze
Taught in: Section 10.1

Adapted from IOAA 2009 (Tehran), theory problem 1. We have restated it in our own words and kept the original data. The solution was last checked on 22 October 2026.

A black hole has mass $1 \times 10^{8} M_{⊙}$ . Calculate its mean mass density inside the Schwarzschild radius, using the spherical volume $4 π R_{s}^{3} / 3$ .

I solved it without the solution

AnswerThe conventional mean density is about 1840 kg/m³. This is a comparison based on mass and horizon radius, rather than a statement that matter fills the interior uniformly.

This problem also appears among the olympiad problems of Section 10.1, Black holes and the Schwarzschild radius, which teaches the ideas it uses. Equation and figure numbers refer to the course.