Question

The volume of a cylinder which exactly fits in a cube of side a is ______.

Answer 1

The volume of a cylinder which exactly fits in a cube of side a is ${\displaystyle \underline{\frac{\pi a^3}{4}}}$.

Explanation:

Since, the cylinder that exactly fits in cube of side a, has its height equal to the edge of the cube and radius equal to half the edge of the cube.

∴ Height = a and radius = ${\displaystyle \frac{a}{2}}$

Now, volume of the cylinder = πr²h

= ${\displaystyle \pi {\left(\frac{a}{2}\right)}^{2}a}$

= ${\displaystyle \frac{1}{4}\pi a^3}$