The surface area and volume of a cube with an edge length of $x \ cm$ are numerically equal. Find the value of $x$.

$A$ cube of side $4 \, cm$ contains a sphere touching its sides. Find the volume of the gap in between. (in $, cm^3$)

$A$ well with $14\, m$ inside diameter is dug $50\, m$ deep. Earth taken out of it is spread all around a rectangular field of length $110\, m$ and width $100\, m$. Find the increase in the height of the field (in $cm$).

Find the total surface area of a hemisphere of radius $42 \, cm$. (in $cm^2$)

The ratio of radii of two cylinders with equal height is $4:5$. What is the ratio of their volumes?

$1\, m^{3} = \dots \, cm^{3}$