Answer:
463.4 m/s
Explanation:
The escape velocity on the surface of a planet/asteroid is given by
(1)
where
G is the gravitational constant
M is the mass of the planet/asteroid
R is the radius of the planet/asteroid
For the asteroid in this problem, we know
is the density
is the volume
So we can find its mass:

Also, the asteroid is approximately spherical, so its volume is given by

where R is the radius. Solving the formula for R, we find its radius:
![R=\sqrt[3]{\frac{3V}{4\pi}}=\sqrt[3]{\frac{3(3.32\cdot 10^{12}m^3)}{4\pi}}=9256 m](https://tex.z-dn.net/?f=R%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%5Cpi%7D%7D%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3%283.32%5Ccdot%2010%5E%7B12%7Dm%5E3%29%7D%7B4%5Cpi%7D%7D%3D9256%20m)
So now we can use eq.(1) to find the escape velocity:
