Multiple choice

If a square with each side 'a' is joined from opposite sides to form a cylinder, then area of each circular end (ignoring units) is

  1. a2

  2. a2/4π

  3. a2/π

  4. a2/4
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B Correct answer
Explanation

When a square of side 'a' is joined at opposite sides to form a cylinder, the height of the cylinder is 'a' and the circumference of the circular base is 'a'. Circumference = 2*pi*r = a, so r = a / (2*pi). Area of circular end = pi*r^2 = pi * (a / (2*pi))^2 = pi * (a^2 / (4*pi^2)) = a^2 / (4*pi).

AI explanation

When a square of side a is rolled into a cylinder, its area forms the curved surface, meaning the height is a and the circumference of the base is also a. Using the circumference formula 2*pi*r = a, the radius of the circular end is calculated as r = a/(2*pi). Applying the circle area formula, the area of each circular end is pi*(a/(2*pi))^2, which simplifies to a^2/(4*pi).

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