Answer:
133.5 m²
Explanation:
the surface area of such a cylinder consists of a top and a bottom, and then a round "mantle", the side wall.
the area of a circle (Ac) is pi×r²
the diagram gives us the diameter of 5m, so the radius is half of it : 2.5m
Ac = 3.14 × (2.5)² = 19.625 m²
what about the "mantle", the round side wall ?
well, you could imagine we simply cut it open.
first, we cut it off the top and the bottom circles.
and the we cut it through the wall from top to bottom in parallel to the inclined side edges (as we can see them when looking at the cylinder directly from the front).
now we can put that cut-open wall flat on the table. and we see a parallelogram.
the area of a parallelogram (Ap) is
Ap = baseline length × height
we know its height, which is exactly also the height of the cylinder = 6m.
and the baseline length is exactly the length of the line we cut along the top or bottom circles, which is the circumference of such a circle.
the circumference of a circle (Cc) is
Cc = baseline length = 2×pi×r = 2×3.14×2.5 = 15.7m
=>
Ap = 15.7×6 = 94.2 m²
so, the total surface area of the cylinder is two times the circle area (for top and bottom) and the wall area
2 × 19.625 + 94.2 = 39.25 + 94.2 = 133.45 = 133.5m²