black hole - Linear extent of an accretion disk

I think the outer edge of an accretion disk is not well-defined, and observationally the radius will depend on which wavelength you consider, since the farther you get from the BH, the softer the radiation will be. But if you look in the UV, then Morgan et al. (2010) find the following relation between $R_{2500}$ (the radius when observed at $lambda = 2500$ Å) and the mass $M_mathrm{BH}$ of the black hole:

$$logleft( frac{R_{2500}}{mathrm{cm}}right) = 15.78 + 0.80 logleft( frac{M_mathrm{BH}}{10^9M_odot}right),$$
(modulo some uncertainties that you can look up in the paper).

That is, if your BH has a mass of $10^8 M_odot$, its radius will be $R_{2500}sim64,mathrm{AU}$, or roughly 1/3 lightdays.

For comparison, its Schwarzschild radius is $sim2,mathrm{AU}$, so your estimate was actually pretty good.

This result is consistent with Edelson et al. (2015), who find 0.35 lightdays, also in the UV. However, in you look in longer wavelengths, the disk is much, much larger. If you're interested beyond your homework assignment, take a look at the accretion disk theory review by Armijo (2013), who shows that in the radio regime, the disk is thousands of AU, and even up to ~100 pc.

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