Answer:
21 units²
Explanation:
the area of a circle is
pi×r²
the lateral area of a cylinder is the area only if the "mantle" of the cylinder : the round area all around the cylinder in its side.
in other words : everything but the ground and the top area.
how can we get the area of the side "mantle" ?
we can imagine, we take a knife and cut a straight line (and at 90°) from the top to the bottom, and then cut off the ground and the top circles by cutting along their circumference.
what do we get ?
if we put that remaining area in the table and press it flat, it is ... a rectangle. simply a rectangle.
its width is the height of the cylinder (the length of our initial top-bottom cut).
and its length is the length of the circle circumference that e just cut off.
and the circumference of a circle is
2×pi×r
so, the lateral area of the cylinder is
2×pi×r × h
r being the radius
h being the height of the cylinder.
and we get
LA = 2×pi×r×r = 882×pi
pi × r² = 441 × pi
r² = 441
r = 21 units²