Diameter in AU of a black hole with given mass?

[PMelol22]

Homework Statement

The Galaxy has a black hole with about 3 x 10^6 M☉. What is its diameter in AU?

Homework Equations

Not sure.

The Attempt at a Solution

3,000,000 solar mass, but not sure how to figure out the diameter in AU. Let's see...diameter of the sun is 1,000,000km

3,000,000 x 1,000,000 = 3 x 10^12 km...one AU is 150 million km...1.5 x 10^8
3x10^12km/1.5x10^8 = 2x10^4 AU??

 

[berkeman]

Homework Statement

The Galaxy has a black hole with about 3 x 10^6 M☉. What is its diameter in AU?

Homework Equations

Not sure.

The Attempt at a Solution

3,000,000 solar mass, but not sure how to figure out the diameter in AU. Let's see...diameter of the sun is 1,000,000km

3,000,000 x 1,000,000 = 3 x 10^12 km...one AU is 150 million km...1.5 x 10^8
3x10^12km/1.5x10^8 = 2x10^4 AU??

Welcome to the PF.

What does your textbook say the relation is between the mass of the BH and its diameter?

Alternately, you can look through the wikipedia article to find that relation... https://en.wikipedia.org/wiki/Black_hole

 

[PMelol22]

I don't see it...

 

[PMelol22]

Is this question about finding the Schwarzschild radius?