Step-by-step explanation:
it seems that the radius of the bottom circle is 3cm.
the surface of a cylinder is the sum of 3 areas :
top
bottom
side wall
top and bottom are circles of identical size.
the area of a circle is
pi × r²
so, in our case, the sum of top and bottom is
2 × pi × r² = 2 × pi × 3² = 2 × pi × 9 = 18pi =
= 56.54866776... cm²
for the side wall just imagine we cut it straight down and off the top and bottom circles and flatten it on the table.
what we get is a rectangle of
circumference of the circle × height of the cylinder
circumference of a circle is
2 × pi × r = 2 × pi × 3 = 6pi
the area of the rectangle (side wall) is then
6pi × 8 = 48pi.
the total surface area is then
18pi + 48pi = 66pi = 207.3451151... cm²
