In the diagram, XY and XprimeYprime are diameters of the two bases of the cylinder, and XY is parallel to XprimeYprime. We know [XYYprimeXprime] = 80. Find the lateral surface area of the cylinder.
+128406 So.....the area of the cross-section [ X Y X' Y'] = 80
This is actually a rectangle that has the dimensions 2r and h
So we have that 2r * h = 80 → rh = 40 → h = 40 / r
The total surface area =
2pi r ( r + h) = 2 pi r ( r + 40/r) = 2 pi r * [ ( r^2 + 40)/r ] = (2pi) ( r^2 + 40) = 2pi r^2 + 80pi
Since 2 pi r^2 is the area of the top and bottom of the cylinder, then 80 pi must be the other part of the surface area = the lateral surface area
