Multiple choice

Find the max.value of the total surface of a right circular cylinder which can be inscribed in a sphere of radius a.

  1. $\displaystyle \pi a^{2}\left ( 1+1/\sqrt{5} \right )$
  2. $\displaystyle \pi/2 a^{2}\left ( 1+\sqrt{5} \right )$
  3. $\displaystyle \pi a^{2}\left ( 1+\sqrt{5} \right )$
  4. $\displaystyle \pi a^{2}\left ( 2+\sqrt{5} \right )$
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C Correct answer
Explanation

Total surface area S = 2 * pi * r^2 + 2 * pi * r * h. For a cylinder in a sphere of radius a, r^2 + (h/2)^2 = a^2. Express S in terms of h, differentiate, and find the maximum. The result is pi * a^2 * (1 + sqrt(5)).

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