Multiple choice

If the volume of sphere and cone are equal with same radius$(r)$ then calculate height$(h)$ of the cone.

  1. $h=4r$
  2. $h=2r$
  3. $h=r$
  4. $h=\dfrac{r}{2}$
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A Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3. Volume of cone = (1/3) * pi * r^2 * h. Equating them: (4/3) * pi * r^3 = (1/3) * pi * r^2 * h. Simplifying gives 4r = h.

AI explanation

The formula for the volume of a sphere is four-thirds pi r cubed, and the formula for the volume of a cone is one-third pi r squared h. Equating the two formulas gives four-thirds pi r cubed equals one-third pi r squared h. Canceling one-third pi r squared from both sides leaves 4r equal to h, meaning the height of the cone is 4r.

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