A cylinder has a volume of 96 pi cubic centimeters and a diameter of 12 centimeters. What is the height of the cylinder in centimeters?

2 2/3 cm

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the volume = 96 pi and the diameter is 12

We want the radius

r = d/2 = 12/2 = 6

96 pi = pi * (6) ^2 h

96 pi = 36 pi h

Divide each side by 36 pi

96 pi/36 pi = 36pi h / 36 pi

8/3 = h

Changing from an improper fraction to a mixed number

2 2/3 = h

Answer: the height of the cylinder is 2.67 centimeters

Step-by-step explanation:

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

From the information given,

volume = 96 pi cubic centimeters

Diameter = 12 centimeters

Radius = diameter/2 = 12/2 = 6 centimeters

Therefore,

96π = π * 6² * h

96π = 36π * h

Dividing the left hand side and the right hand side of the equation by 36π, it becomes

96π/36π = 36π/36π * h

h = 2.67 centimeters