star - Rate of Mass Loss from the Solar Wind

This is problem 1-4 from Principles of Stellar Evolution and Nucleosynthesis by Clayton:

Assuming at the Earth a characteristic velocity of 400km/s and density of 10amu/cm$^{3}$ for the solar wind, calculate the rate of mass loss for the sun.

There weren't any formulas about this in the section so I made a stab at it with dimensional analysis.

$$frac{dM}{dt} = frac{rho V}{Delta t} = rho v A$$
$$frac{dM}{dt} = left( frac{10 amu}{cm^{3}} right) left( frac{400km}{s} right) left( frac{4 pi (6.96e10 cm)^{2}}{1} right) left( frac{10^{5}cm}{km} right) left(frac{10^{-24} g}{1 amu} right) left( frac{M_{odot}}{2 times 10^{33} g} right) left( frac{3600s}{hr} right) left( frac{24 hr}{day}right)left(frac{365day}{yr}right)$$
$$frac{dM}{dt} = 3.84 times 10^{-19} M_{odot} / yr$$

However, the answer given in the book is $0.4 times 10^{-13} M_{odot} / yr$. So, I'm off by about five magnitudes. Can anyone point out where I went wrong and/or point me in the correct direction?

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