Question

# Calculate the Density of an steroid An extremely massive (spherical) asteroid with a mass of 8.7...

Calculate the Density of an steroid

An extremely massive (spherical) asteroid with a mass of 8.7 x 1015 kg passes through the atmosphere and hits the Caspian Sea. The diameter of the asteroid is determined to be 20.5 km and there are initially 78200 km3 of water in the Caspian Sea. Assuming that this asteroid is denser than water, calculate the water displacement in cubic meter. What is the density of the asteroid in g/cm3? (Hint: use the equation for the volume of a sphere)

Solution :-

Mass of asteroid =8.7*10^15 kg * 1000 g / 1 kg = 8.7*10^18 g

= 20.5 km / 2 = 10.25 km

10.25 km * 1000 m / 1 km = 10250 m

Now lets calculate the volume of the asteroid

V= 4/3 pi r3

V = 4/3 * 3.14 * (10250 m)^3

= 4.509*10^12 m3

The volume of water displaced is same as the volume of the asteroid so it displaces 4.509*10^12 m3 water

Now lets convert the volume of asteroid from m3 to cm3

4.509*10^12 m3 * 1*10^6 cm3 / 1 m3 = 4.509*10^18 cm3

Now lets calculate the density

Density = mass / volume

= 8.7*10^18 g / 4.509*10^18 cm3

= 1.929 g/cm3

So the density of the asteroid isd 1.929 g/cm3