Multiple choice

If a sphere of radius r entered in side a cylinder tightly the volume of the cylinder is?

  1. $\pi r^{2}h$
  2. $2\pi r^{2}h$
  3. $3\pi r^{3}$
  4. $2\pi r^{3}$
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D Correct answer
Explanation

A sphere fitting tightly inside a cylinder gives the cylinder radius r and height 2r, equal to the sphere's diameter. Therefore, its volume is πr^2 × 2r = 2πr^3.

AI explanation

When a sphere of radius r fits tightly inside a cylinder, the height of the cylinder equals the diameter of the sphere, meaning h = 2r. Applying the volume of a cylinder formula V = pi * r^2 * h, we substitute 2r for h to get V = pi * r^2 * 2r. Multiplying the terms gives the final volume of 2 * pi * r^3.

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