Answer: To find the surface area of a cylinder, we need to add the areas of the top and bottom circles to the lateral surface area (the curved surface that connects the circles).
1.) Given that the diameter (d) of the cylinder is 10m and the height (h) is 8m.
First, let's find the radius of the cylinder (r):
r = d/2 = 10m/2 = 5m
Then, we can find the surface area of the cylinder:
The area of each circle is given by A = πr^2
A(top and bottom circles) = 2π(5m)^2 = 2π(25m^2) = 50πm^2
The lateral surface area is given by A = 2πrh
A(lateral) = 2π(5m)(8m) = 80πm^2
The total surface area is the sum of the areas of the top and bottom circles and the lateral surface area:
A(total) = A(top and bottom circles) + A(lateral)
A(total) = 50πm^2 + 80πm^2
A(total) = 130πm^2
Therefore, the surface area of the cylinder is 130π square meters (or approximately 408.4 square meters if you round to one decimal place).