Question

The two spheres above have the same center. One has a radius of 4 cm, and the other has a radius of 5 cm. Approximately how much space is in between the two spheres?

Answer 1

The space between the two spheres will be the volume of the larger sphere minus the volume of the smaller sphere.  Given that the volume of any sphere is:

V=(4πr^3)/3  The space between to sphere of different radius and positioned about the same center is:

S=(4πR^3)/3-(4πr^3)/3  I used S=volume of space, R=larger radius and r=smaller radius...

S=(4π/3)(R^3-r^3), we are told that R=5 and r=4 so

S=(4π/3)(5^3-4^3)

S=(4π/3)(125-64)

S=(4π/3)(61)

S=244π/61

S=4π cm^3

S≈12.57 cm^3  (to nearest hundredth of a ml)