Multiple choice

The rectangle of perimeter 36 cm is revolved about one side to form a cylinder of maximum volume. The length and breath of the rectangle are in the ratio.

  1. 1 : 1

  2. 1 : 3

  3. 2 : 3

  4. 2 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let sides be L and B. 2(L+B) = 36, so L+B = 18. Volume V = pi * r^2 * h. If revolved about L, V = pi * B^2 * L = pi * B^2 * (18-B). To maximize, dV/dB = pi * (36B - 3B^2) = 0, so 3B(12-B) = 0, B=12, L=6. Ratio L:B = 6:12 = 1:2. If revolved about B, L=12, B=6, ratio 2:1.

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