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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 four inches. What is the original radius in inches?

 May 6, 2021
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Volume of a cylinder =   pi r^2 h

 

pi (r+6)^2 * 4  = pi r^2 (h+6)      eliminate pi

(r^2 + 12r + 36)   * 4   = 10 r^2

6r^2 - 48r - 144 = 0

 

r^2 - 8r -24 = 0          quadratic formula shows r = 4 + 2 sqrt 10   =   10 .32455532

 May 6, 2021

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