What is the total surface area in square metres of a closed cylinder that is 5 m high and 5 m in diameter?

To find the total surface area of a closed cylinder, you need to consider both the lateral surface area and the areas of the top and bottom circular bases. The formula for the total surface area ( A ) of a closed cylinder is given by:

[ A = 2\pi r(h + r) ]

where ( r ) is the radius and ( h ) is the height of the cylinder.

In this case, the diameter of the cylinder is given as 5 m, which means the radius ( r ) would be half of that, so ( r = 2.5 ) m. The height ( h ) is provided as 5 m.

Now, we can substitute the values into the formula:

1. Calculate the lateral surface area:

[

Lateral\ Surface\ Area = 2\pi rh = 2\pi(2.5)(5) = 25\pi , \text{m}^2

]

2. Calculate the area of the two bases:

[

Area\ of\ Bases = 2\pi r^2 = 2\pi(2.5)^2 = 2\pi(6.