Multiple choice

A right circular cylinder is to be made so that the sum of its radius and its height is 9 ft. The maximum volume of the cylinder can be

  1. 54 π ft3

  2. 108 π ft3

  3. 81π ft3

  4. 72 π ft3

  5. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let r be the radius and h be the height. We have r + h = 9, so h = 9 - r. The volume V = pi * r^2 * h = pi * r^2 * (9 - r) = pi * (9r^2 - r^3). Taking the derivative with respect to r and setting it to 0 gives 18r - 3r^2 = 0, so r = 6 and h = 3. The maximum volume is pi * 6^2 * 3 = 108pi.

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