Step-by-step explanation:
the surface area of a cylinder consists of 3 parts :
the top and the bottom circles, and the "wall" or "mantle" all around the side.
the area of a circle is
pi×r²
with r being the radius.
in our case
pi×4² = 16pi = 50.26548246 ... cm²
since we have 2 circles (top and bottom), this is
100.5309649... cm²
and the mantle area :
if you cut it open and put it flat on a table, it is simply a rectangle with the cylinder height being the width, and the circle circumference being the length.
so, the circumference of a circle is
2×pi×r
in our case
2×pi×4 = 8pi = 25.13274123... cm
and so the area of the mantle or wall is
25.13274123... × 8 = 201.0619298... cm²
all together the whole cylinder surface area is
201.0619298... + 100.5309649... =
= 301.5928947... cm²
so, wherever your teacher rounded in the process (which explains the little difference), but the first answer option (301.44) must be correct.
