Multiple choice

The height $h$ of a cylinder is equal to the edge of a cube. If the cylinder and the cube have the same volume, what is the radius of the cylinder?

  1. $\displaystyle \frac { h }{ \sqrt { \pi } } $
  2. $\displaystyle h\sqrt { \pi } $
  3. $\displaystyle \frac { \sqrt { \pi } }{ h } $
  4. $\displaystyle \frac { { h }^{ 2 } }{ \pi } $
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A Correct answer
Explanation

Let the cube edge be s. Volume of cube = s^3. Volume of cylinder = pi * r^2 * h. Given h = s, so volume of cube = h^3. Equating the volumes: pi * r^2 * h = h^3. Dividing by pi * h gives r^2 = h^2 / pi, so r = h / sqrt(pi).

AI explanation

The volume of a cube with edge h is h^3, and the volume of a cylinder is πr^2h. Setting the two volumes equal gives πr^2h equals h^3. Dividing both sides by πh leaves r^2 equals h^2 divided by π. Taking the square root of both sides gives the radius r equals h divided by the square root of π.

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