Question

Question 36

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

Answer 1

$\frac{\pi a^3}{4}$
Since, the cylinder that exactly fits the cube of side a has its height equal to the edge of the cube and radius equal to half the edge of the cube.
$\therefore$ Height = a and radius $=\frac{a}{2}$
Now, volume of the cylinder $=\pi r^{2}h=\pi {\left(\frac{a}{2}\right)}^{2}a$
$=\frac{1}{4}\pi a^3$