a cylinder has a radius of r and a height of h. A rectangular box has a length of r, a width of h and height of h. Their combined volume is V=πr^2h+h^2r If their combined volume is 600 cubic inches and h is 5 inches, solve for the radius(r). Round your answer to 2 decimals.
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So you have 600 = pi* r^2 * 5 + 5^2 * r = 5*pi* r^2 + 25 * r. Rewrite this as 5pi * r^2 + 25 * r - 600 = 0 and then use the quadratic equation to solve for r. This gives r=(-25 +/- sqrt(25^2 - 4*(5pi)*(-600)))/10pi which gives either r = 5.44 or r = -7.03. We need r to be positive so the answer is r = 5.44 inches. (Test this value in the original formula for V to see if it works just to be sure. It works. :) )