A cylinder and a sphere both have the same radius, 4. The height of the cylinder is equal to the diameter of the sphere. Select the expression that describes the volume of the cylinder that is not occupied by the sphere.

134.04 cubic units

Step-by-step explanation:

Step 1

Find the Volume of the Sphere

Formula = 4/3πr³

r= radius = 4

Hence,

Volume = 4/3 × π × 4³

= 268.08 cubic units

Step 2

Find the Volume of the cylinder

Formula = πr²h

r = radius = 4

h = Height = Diameter of the sphere

Radius of a sphere = 4

Diameter = Height of cylinder = 2 × r = 2 × 4 = 8

Hence: π × 4² × 8

= 402.12 cubic units

Step 3

The expression that describes the volume of the cylinder that is not occupied by the sphere = Volume of Cylinder - Volume of sphere

= 402.12 cubic units - 268.08 cubic units

= 134.04 cubic units

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

answer: the answer is 35%