Multiple choice

A right circular cylinder just encloses a sphere of radius a cm, then the curved surface area of the cylinder is :

  1. $4 \pi a^2 cm$
  2. $2 \pi a^2 cm^2$
  3. $3 \pi a^2 cm$
  4. $8 \pi a^2 cm^2$
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A Correct answer
Explanation

A cylinder that just encloses a sphere of radius a has cylinder radius a and height 2a. Its curved surface area is 2pi x a x 2a = 4pi a^2.

AI explanation

If a right circular cylinder just encloses a sphere of radius a, the cylinder must have a radius of a and a height equal to the sphere's diameter, which is 2a. The curved surface area of a cylinder is 2 * pi * r * h, so substituting the radius and height gives 2 * pi * a * 2a. This simplifies to 4 * pi * a^2 square cm.

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