To find the height of the rain barrel, we need to use the formula for the surface area of a cylinder.
The surface area of a cylinder is given by 2πr^2 + 2πrh, where r is the radius of the cylinder and h is the height. We know the diameter of the cylinder (1.2 meters), so we can find the radius by dividing the diameter by 2. The radius is 1.2/2 = 0.6 meters.
Plugging the values into the formula for surface area, we get:
2π * 0.6^2 + 2π * 0.6 * h = 9.0432
Expanding the first term:
2π * 0.6^2 = 2.25 * π
Substituting this value into the equation:
2.25 * π + 2π * 0.6 * h = 9.0432
Dividing both sides by 2π * 0.6:
2.25 + h = 9.0432 / (2 * π * 0.6)
Solving for h:
h = (9.0432 / (2 * π * 0.6)) - 2.25
The height of the rain barrel is approximately 0.73 meters