I need help
People hate opening attachments here. so you would do well in the future not to use them.
think of breaking the cylinder in pieces. the ends are circles, and we know the area for circles, so that is good. as for the cylinder, we can cut in along the length and flatten it so that it s a rectangle. the length will be the circumference of the circle and the width will be $\displaystyle a$
so we get, the surface area is given by:
$\displaystyle A = \underbrace{ \pi r^2 + \pi r^2}_{\mbox{Area of both ends}} +\underbrace{ 2 \pi r a}_{\mbox{Area of the cylinder without the ends}} = 2 \pi r (r + a)$
i hope you see why. here, r is the radius, which is b/2 since b is the diameter