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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.

 

 Nov 15, 2020
 #1
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Here is the diagram.

 

 Nov 15, 2020
 #2
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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

 

 

cool cool cool

 Nov 15, 2020

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