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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

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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