Question 961500

 Well if you can make the cylinder with the rectangle and the two circles, you can use them to derive the surface area of the cylinder.

The area of the two circles is straightforward. The area of one circle is {{{pi *r^2}}}, so for two circles, you get {{{2 * pi * r^2}}}

-the longest side or folded side of the rectangle must be equal to {{{2 * pi * r}}}, which is the circumference of the circle

To get the area of the rectangle, multiply {{{h}}} by {{{2* pi * r}}} and that is equal to {{{2 * pi * r *h}}}.

Therefore, the total surface area of the cylinder, call it {{{SA}}} is:

{{{SA = 2 * pi * r^2 +   2 * pi * r *h}}}........plug in given values {{{r = 7cm}}} and {{{h = 5cm}}}


{{{SA = 2 * 3.14 * (7cm)^2 +   2 * 3.14*(7cm) *(5cm)}}}

{{{SA = 6.28 * 49cm^2 +   6.28*7cm *5cm}}}

{{{SA = 307.72cm^2 +  219.8cm^2}}}

{{{SA = 527.52cm^2}}}