Prisms are 3D shapes whose cross-sectional area never varies. A Cylinder is just a special type of prism. 

If you painted a 3D object, the surface area would be the 2D area all round the outside that you actually paint.

To work out the surface area of a prism, you have to work out the area of each face separately, then add up all the areas you get.

 

But how do you find the area of a cylinder?

Imagine rolling the cylinder out, you get a large rectangle with a circle at either end, which are the bases of the prism. 

By looking at it this way, we can see that the ends of the rectangle have the same length as the circumference of the circle.

So the area of a the rectangle part is ( l x 2πr ), where l = length of rectangle

The area of a circle is πr2.

So the area of a cylinder is area of 2 circles + area of rectangle 

A = 2πr2 + 2πrl = 2πr (r+l) 

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