+0  
 
+1
46
1
avatar

Either increasing the radius or the height of a cylinder by six inches will result in the same volume. The original height of the cylinder is two inches. What is the original radius?

 May 28, 2020
 #1
avatar
0

 

Either increasing the radius or the height of a cylinder by six inches will result in the same volume. The original height of the cylinder is two inches. What is the original radius?  

 

Volume of a Cylinder  =  π • r2 • h   

 

If you increase the radius by 6 the new volume will be   π • (r+6)2 • 2  

If you increase the height by 6 the new volume will be   π • r2 • (2+6)  

 

Set the new volumes equal and solve for r  

 

                                                                                     π • (r2 + 12r + 36) • 2  =  π • r2 • 8   

First, let's divide both sides by π                                        (r2 + 12r + 36) • 2  =        r2 • 8   

Next, let's divide both sides by 2                                          r2 + 12r + 36         =        r2 • 4   

Subtract r2 from both sides                                                         12r + 36         =        3r2     

Subtract (12r + 36) from both sides                                                    0             =        3r2 – 12r – 36

 

Switch sides, just cuz I prefer the zero on the right             3r2 – 12r – 36  =  0   

Factor the quadratic                                                            (3r + 6)(r – 6)  =  0    This is the hardest step, IMHO.

 

Set each factor equal to zero                                                3r + 6   =  0 

                                                                                                      r  =  –2             Discard... can't have negative radius.

 

                                                                                                 r – 6  =  0 

                                                                                                       r  =  6              The original radius was 6.   . 

.

 May 29, 2020

12 Online Users

avatar
avatar
avatar