SOLUTION: Find the outside surface area. Note that the cylinder does not have a top. (Assume a = 2 cm and b = 9 cm. Find the exact solution or round your answer to three decimal places.)

Question 765577: Find the outside surface area. Note that the cylinder does not have a top. (Assume a = 2 cm and b = 9 cm. Find the exact solution or round your answer to three decimal places.)

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
The surface area of a cylinder can be found by breaking it down into three parts:
The two circles that make up the ends of the cylinder.
The side of the cylinder, which when "unrolled" is a rectangle
The area of the rectangle is the width times height.
The area of a circle is , so the combined area of the two disks is twice that, or .
The width is the height of the cylinder, and the length is the distance around the end circles.
This is the circumference of the circle and is . Thus the rectangle's area is .
so,
since your cylinder does not have a top, the surface area will be

if your and , then we have

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