Answer:
18.65 cm
Step-by-step explanation:
the surface area of a cylinder is the combination of the two circles (1 at the top, 1 at the bottom) and the area of the side wall or "mantle".
so, two equally sized circle areas and the side area.
this side area is nothing else than a rectangle that is bent around and connected to the circumference of both circles. therefore, the side lengths of this rectangle must be the cylinder height and the length of the circumference of the circles.
that is also why we need the cylinder height to get its surface area (and also volume by the way).
circle area : pi × r²
rectangle area : length × width
cylinder surface area = 2 circle areas + side rectangle area
=> 1800 = 2 × (pi×r²) + (2×pi×r)×h = 2×pi×100 + 2×pi×10×h
=> 1800 = 200×pi + 20×pi×h
=> (1800 - 200×pi) = 20×pi×h
=> (1800 - 200×pi) / (20×pi) = h = 18.65 cm
