Available evidence suggests that about 20 percent of the asteroid’s mass turned to dust and spread uniformly over Earth after eventually settling out of the upper atmosphere. This dust amounted to about 0.02 g/cm^2 of Earth’s surface. The asteroid very likely had a dentistry of about 2 g/cm^3. Calculate the mass (in kilograms and tons) of the asteroid and its radius in meters, assuming that it was a sphere. (the area of Earth is 5.1 x 10^14 m^2; 1 lb = 453.6 g.)

Question

Available evidence suggests that about 20 percent of the asteroid’s mass turned to dust and spread uniformly over Earth after eventually settling out of the upper atmosphere.  This dust amounted to about 0.02 g/cm^2 of Earth’s surface.  The asteroid very likely had a dentistry of about 2 g/cm^3.  Calculate the mass (in kilograms and tons) of the asteroid and its radius in meters, assuming that it was a sphere.  (the area of Earth is 5.1 x 10^14 m^2; 1 lb = 453.6 g.)

I got a mass of 5.1 x 10^14 kg
a radius of 3.9 x 10^3 m
a mass of 5.6 x 10^11 short tons

the back of the book says
5.0 x 10^14 kg
5.5 x 10^11 short tons
4 x 10^3 m

I don't see how to get those answers and don't see what I have done wrong

Anonymous · Answer

i got 5.1 x 10^30 kg and r = 1.8 x 10^24