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If the diameter of a right cylindrical can with circular bases is increased by 25%, by what percent should the height be decreased in order to preserve the volume of the original can?

 Nov 27, 2020
 #1
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The height should be decreased by 28%.

 Nov 27, 2020
 #2
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Call the volume  of  the original can     pi * r^2 * h

 

If the diameter is increased by 25 %  then so is the radius

 

So  we want to know this

 

pi * r^2 * h  =  pi *  (1.25 r)^2   (1 - a)  * h       where a is the % of height decrease

 

1  =  1.5625  (1 - a)

 

1/ 1.5625  =  ( 1 - a)  = 

 

.64  = 1 - a      rearrange as

 

a = 1 - .64  = .36   ......the height should be decreased by 36%

 

 

cool cool cool

 Nov 27, 2020

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