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.