Final answer:
To find the height and diameter of the cylinder, solve for the radius first using the surface area formula. Substitute the height with 3 times the radius and solve the equation to get the value of the radius. Use the radius to calculate the height and diameter by multiplying it by 3 and 2 respectively.
Step-by-step explanation:
To find the height and diameter of the cylinder, we need to solve for the radius first. We know that the surface area of the cylinder is about 155.83 square feet, which is equal to the sum of the areas of the two end-caps and the curved surface.
Let's assume the radius of the cylinder is 'r' feet. Since the height of the cylinder is 3 times the radius, the height would be 3r feet.
Using the formula for surface area of a cylinder, we can set up the equation: 2πr² + 2πrh = 155.83.
Since the height is 3 times the radius, we can substitute 3r for h in the equation. Solving this equation will give us the radius and then we can calculate the height and diameter by multiplying the radius by 3 and 2 respectively.