A sphere is inside a cube. The diameter of the sphere is equal to the edge length of the cube. What portion of the volume of the cube is taken up by the sphere? Options: 1/8, 3/8, 2pi/16, pi/16, pi/48.

Answer: pi/6

Step-by-step explanation:

Since the sphere is inside a cube and the diameter of the sphere is equal to the edge length of the cube, then, the portion of the volume of the cube taken up by the sphere will be the volume of the sphere

Volume of a sphere = 4/3πr^3

A cube has all three dimensions of the same length and it is called the side length of the cube.

Given that a sphere is inside a cube and the diameter of the sphere is equal to the edge length of the cube.

Diameter = length

D = l

Volume of cube = l^3

Radius of the sphere = D/2 = l/2

V = 4/3πr^3

V = 4/3π (l/2) ^3

V = 4/3π (l^3/8)

But V = l^3 = volume of the cube

V = π/6V