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The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meters and the diameter of a base of the cylinder is 4 meters. What is the height of the cylinder? Enter your answer, as a simplified fraction, in the box.

User Gibson
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Answer: The Height of the cylinder is 4 meters.

Step-by-step explanation: The surface area of a cylinder can be represented by the formula:

SA = 2πr² + 2πrh

Where SA is the surface area, r is the radius of the base, and h is the height of the cylinder.

We know that the surface area is 24π m², and the distance around the base (circumference) is 3π meters. We can use the formula for circumference, C = 2πr, to find the radius.

3π = 2πr

r = 3/2

We also know that the diameter of the base is 4 meters. Since the diameter is twice the radius, we can divide 4 by 2 to find the radius:

r = 4/2 = 2

Now we can substitute this value of r back into the formula for surface area, and solve for h:

24π = 2π(2²) + 2π(2)h

24π = 8π + 4πh

24π - 8π = 4πh

16π = 4πh

h = 16/4 = 4

So the height of the cylinder is 4 meters.

User Abinesh Joyel
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