Multiple choice

A rectangle of sides 10 cm and 8 cm is folded to form a cylinder in two different ways. The volume of the bigger cylinder thus formed is

  1. $\displaystyle \dfrac{175}{\pi }cm^{3} $
  2. $\displaystyle \dfrac{150}{\pi }cm^{3} $
  3. $\displaystyle \dfrac{200}{\pi }cm^{3} $
  4. $\displaystyle \dfrac{160}{\pi }cm^{3} $
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C Correct answer
Explanation

Folding a 10x8 rectangle into a cylinder: Case 1 (height 8, circumference 10): r = 10/(2*pi) = 5/pi. Volume = pi * r^2 * h = pi * (25/pi^2) * 8 = 200/pi. Case 2 (height 10, circumference 8): r = 8/(2*pi) = 4/pi. Volume = pi * (16/pi^2) * 10 = 160/pi. The bigger volume is 200/pi.

AI explanation

When the rectangle is folded into a cylinder, the larger cylinder is formed by rolling the 10 cm side into the base circumference, making the height 8 cm. Setting the circumference 2 * pi * r equal to 10 gives a base radius of 5/pi cm. The volume of a cylinder is V = pi * r^2 * h, so substituting the values gives V = pi * (5/pi)^2 * 8. This simplifies to pi * (25/pi^2) * 8, which results in a volume of 200/pi cubic centimeters.

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