Answer: The total surface area of the cylinder is 850π m².
Explanation:
The cylinder has a curved surface area of 408π m², which is the area of the lateral surface of the cylinder. The lateral surface of a cylinder is the curved surface that connects the top and bottom bases of the cylinder.
The formula for the lateral surface area of a cylinder is given by: Lateral Surface Area = 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder.
We are given that the length of the cylinder is 17 m. Since the length of a cylinder is the same as its height, we can substitute h = 17 m into the formula for the lateral surface area to get:
408π m² = 2πr(17 m)
Simplifying this equation, we get:
r = 12 m
Now that we know the radius of the cylinder, we can find the total surface area of the cylinder. The formula for the total surface area of a cylinder is given by:
Total Surface Area = 2πr(r + h)
Substituting r = 12 m and h = 17 m into this formula, we get:
Total Surface Area = 2π(12 m)(12 m + 17 m) = 850π m²
Therefore, the total surface area of the cylinder is 850π m².