To find the total surface area of a right circular cylinder, we need to calculate the sum of the areas of the curved surface (lateral surface) and the two circular bases.
The formula for the lateral surface area of a cylinder is given by:
Lateral Surface Area = 2πrh
The formula for the area of a circular base is:
Base Area = πr^2
Given
Radius (r) = 708 in
Height (h) = 229 in
Calculate the surface area:
Lateral Surface Area = 2πrh = 2 * 3.14159 * 708 * 229
Base Area = πr^2 = 3.14159 * 708^2
Total Surface Area = Lateral Surface Area + 2 * Base Area
Calculate the values:
Lateral Surface Area = 2 * 3.14159 * 708 * 229 = 1020545.72284 in² (rounded to 5 decimal places)
Base Area = 3.14159 * 708^2 = 1577589.392 in² (rounded to 3 decimal places)
Total Surface Area = 1020545.72284 + 2 * 1577589.392 = 4175724.50784 in² (rounded to the nearest ten thousand)
Therefore, the total surface area of the right circular cylinder with a radius of 708 in and a height of 229 in is approximately 4,175,700 in².