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.)

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> 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.)       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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 r%5E2%2Api, so the combined area of the two disks is twice that, or 2r%5E2%2Api.
The width is the height h of the cylinder, and the length is the distance around the end circles.
This is the circumference of the circle and is 2%2Api%2Ar. Thus the rectangle's area is 2%2Api%2Ar+%2A+h.
so, SA=2r%5E2%2Api%2B2%2Api%2Ar+%2A+h
since your cylinder does not have a top, the surface area will be
SA=r%5E2%2Api%2B2%2Api%2Ar+%2A+h
if your a=r=2cm and b=h+=9cm, then we have

SA=%282cm%29%5E2%2A3.142%2B2%2A3.142%2A2cm+%2A9cm

SA=4cm%5E2%2A3.142%2B6.284%2A18cm%5E2

SA=12.568cm%5E2%2B113.112cm%5E2

SA=125.68cm%5E2