Multiple choice

If the height of cylinder becomes $4$ times of original height and radius is doubled, then which of following will be true?

  1. Volume of the cylinder will be $16$ times.

  2. volume of cylinder remain unchanged.

  3. Volume of cylinder will be halved.
  4. Volume of cylinder will be $\displaystyle\frac{1}{4}$ of original volume.
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A Correct answer
Explanation

Volume = pi * r^2 * h. New volume = pi * (2r)^2 * (4h) = pi * 4r^2 * 4h = 16 * (pi * r^2 * h). The volume becomes 16 times the original.

AI explanation

The volume of a cylinder is found by the formula pi times r squared times h. When the height becomes 4 times the original and the radius is doubled, the new volume is pi times the quantity 2r squared times 4h, which simplifies to 16 times pi times r squared times h. Therefore, the new volume of the cylinder will be 16 times the original volume.

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