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The surface area of a solid cylinder is found using the formula $SA = 2\pi r^2 + 2\pi rh$. The volume of a cone is found using the formula $V = \frac{1}{3} \pi r^2 h$. Judy has a solid cylinder whose total surface area is numerically equal to the volume of a particular cone that has a base congruent to the cylinder's base. If the height of both solids is $6$ inches, what is the radius?

 Aug 25, 2023
 #1
avatar+126971 
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Filling in for the  height  we  have the  following equation

 

2pi *r^2 + 2pi * r * 6 =     (1/3) pi * r^2 * 6     simplify

 

2pi * r^2 + 12 pi * r  =  2 pi * r^2              subtract 2pi *r  from both sides

 

12 pi * r =  0

 

r =  0     

 

In other words......this  problem is  impossible

 

 

cool cool cool

 Aug 25, 2023

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