Question

A cylinder with a radius of 4 cm and a height of 6-cm is inside of a

sphere with a radius of 10 cm. How much space is inside the sphere,
but outside the cylinder? Round to the nearest tenth if necessary. Use 3.14 for π.

Answer 1

To find the space inside the sphere but outside the cylinder, we need to subtract the volume of the cylinder from the volume of the sphere.

The volume of the cylinder is given by:

V_cylinder = πr^2h

Substituting the given values, we get:

V_cylinder = π(4^2)(6) = 96π cubic cm

The volume of the sphere is given by:

V_sphere = (4/3)πr^3

Substituting the given value, we get:

V_sphere = (4/3)π(10^3) = (4000/3)π cubic cm

The space inside the sphere but outside the cylinder is therefore:

V_space = V_sphere - V_cylinder

V_space = (4000/3)π - 96π

V_space = (4000/3 - 288)π

V_space ≈ 869.6 cubic cm (rounded to the nearest tenth)

Therefore, the space inside the sphere but outside the cylinder is approximately 869.6 cubic cm.