Respuesta :
We have been given that a large sphere has a diameter of 20 feet. A smaller sphere with a radius of 4 feet is cut out of the center of the larger sphere. We are asked to find the volume outside smaller sphere and inside larger sphere.
The volume outside smaller sphere and inside larger sphere will be equal to volume of larger sphere minus volume of smaller sphere.
[tex]V=\frac{4}{3}\pi R^3-\frac{4}{3}\pi r^3[/tex], where,
R = Radius of larger sphere,
r = Radius of smaller sphere.
We know that radius is half the diameter, so radius of larger sphere would be [tex]R=\frac{20}{2}=10[/tex].
Since the smaller sphere has a radius of 4 feet, so [tex]r=4[/tex].
Upon substituting these values in above formula, we will get:
[tex]V=\frac{4}{3}\pi (10)^3-\frac{4}{3}\pi(4)^3[/tex]
Therefore, the volume outside smaller sphere and inside larger sphere would be [tex]\frac{4}{3}\pi (10)^3-\frac{4}{3}\pi(4)^3[/tex] and option B is the correct choice.
