To find the total surface area of the cylinder, add the curved surface area and the areas of the two circular ends. The total surface area is found to be approximately 466.47 m².
Step-by-step explanation:
To find the total surface area of the cylinder, you need to sum up the curved surface area and the areas of the two circular ends. The curved surface area of the cylinder is given as 408 m². The formula for the curved surface area of a cylinder is given by 2πr×h, where r is the radius and h is the height. Since the length of the cylinder is given as 17 m, we can assume length and height to be the same.
By substituting the known value of the curved surface area, we can solve for r:
408 = 2πr×17
r = 408 / (2π×17)
r ≈ 3.043
The radius of the cylinder is approximately 3.043 m. Now, we can calculate the total surface area:
Total Surface Area = Curved Surface Area + 2×πr2
Total Surface Area = 408 + 2×π(3.043)2
Total Surface Area ≈ 408 + 58.47
Total Surface Area ≈ 466.47 m²