Step-by-step explanation:
this is a combination of a half-sphere (radius 5 m) and a cone (base radius 5 m, height 11 - 5 = 6 m).
the circle they are sharing in the middle is not part of the surface of the combined object.
the surface of a sphere is
4×pi×r²
we only need half of it here, so the surface area of a half-sphere is
2×pi×r²
which is in our case
2×pi×5² = 50pi = 157.0796327... m²
the surface of a cone is
pi×r×(r + sqrt(h² + r²)) = pi×r² + pi×r×sqrt(h² + r²)
the first term there is the area of the base circle, which we don't need.
so, the outside surface area of the cone is
pi×r×sqrt(h² + r²) = pi×5×sqrt(6² + 5²) =
= pi×5×sqrt(36 + 25) =
= pi×5×sqrt(61) = 122.683115... m²
together, the surface area is then
157.0796327... + 122.683115... = 279.7627477... m²