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The cylinder in a sphere have the same radius for the height of the cylinder is equal to the diameter of the spear select the expression that describes the volume of the cylinder that is not occupied by the sphere

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The volume of the cylinder that is not occupied by the sphere is 2πr³/3

Since the object is a sphere in a cylinder, we need to know the volume of sphere and cylinder.

What is volume of a cylinder?

The volume of a cylinder is given by V '= πr²h where

  • r = radius of cylinder and
  • h = height of cylinder.

Since the height of the cylinder equals the diameter of the sphere, h = 2r

So, V' = πr²h

V' = πr² × 2r

V' = 2πr³

What is volume of sphere?

The volume of a sphere of radius r is given by V = 4πr³/3

Volume of cylinder not occupied by sphere

The volume of the cylinder not occupied by the sphere is V" = V' - V

=  2πr³ - 4πr³/3

= (6πr³ - 4πr³)/3

= 2πr³/3

So, the volume of the cylinder that is not occupied by the sphere is 2πr³/3

Learn more about volume of cylinder here:

https://brainly.com/question/27535498

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