Answer:
Density is 16.11 units, If it is less than the density of water in the same units, the sphere will float.
Step-by-step explanation:
We have to:
Mass of shell at distance r from:
Density = mass / volume, if we solve for mass we have:
Mass = volume * density
replacing:
Mass = (4 * pi * (r ^ 2) * dr) * (0.39r ^ 2)
Mass = 1.68 * pi * r ^ 4 * dr
Mass = 1.68 * pi integral from 2 to 8 of {r ^ 4 * dr}
Mass = 1.68 * 3.14 * (r ^ 5) / 5 when r equals 2 to 8, replacing:
Mass = 1.68 * 3.14 * [(8 ^ 5/5 - (2) ^ 5/5]
Mass = 34537.79
Now the volume would be: (4/3) * pi * r ^ 3, we replace:
(4/3) * 3.14 * 8 ^ 3 = 2143.57
Density = 34537.79 / 2143.57 = 16.11 units
If it is less than the density of water in the same units, the sphere will float.
