Multiple choice

A rectangular metal sheet of area $\displaystyle { 2\ m }^{ 2 }$ is rolled to form a cylinder of volume $\displaystyle { \frac { 4 }{ \pi } \ m^{ 3 } } $. Then the radius of cylinder thus formed is ______ m.

  1. $\displaystyle \dfrac 4 {\pi} $
  2. $\displaystyle \dfrac  {\pi} 4 $
  3. $\displaystyle \pi $
  4. $\displaystyle {\pi}^{2} $
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A Correct answer
Explanation

A sheet of area 2 rolled into a cylinder implies the lateral surface area is 2 = 2*pi*r*h. Volume = pi*r^2*h = 4/pi. From the first, h = 1/(pi*r). Substituting into volume: pi*r^2*(1/(pi*r)) = r = 4/pi.

AI explanation

Let the radius of the cylinder be r and its height be h, where its volume is pi*r^2*h = 4/pi. The lateral surface area of the cylinder is 2*pi*r*h, which is given as 2 m^2. From the lateral area equation, h = 1/(pi*r). Substituting this expression for h into the volume equation yields pi*r^2*(1/(pi*r)) = 4/pi, which simplifies to r = 4/pi. The correct result is 4/pi.

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