The height of the cylinder is approximately 7.94 meters when rounded to the nearest tenth.
How did this do?
The surface area of a cylinder can be calculated using the formula:
SA = 2πr^2 + 2πrh
where r is the radius of the base and h is the height of the cylinder.
We are given the diameter of the cylinder's base, which is 8 m. The radius is half the diameter, so:
r = 8 m / 2 = 4 m
Substituting this value for r, and the given value for SA into the formula, we get:
256.224 m² = 2π(4 m)^2 + 2π(4 m)h
Simplifying this equation:
256.224 m² = 32π + 8πh
256.224 m² - 32π = 8πh
h = (256.224 m² - 32π) / (8π)
h ≈ 7.94 m (rounded to the nearest tenth)