Question

A student is trying to remember some formulas from geometry. in what follows, assume a is area, v is volume, and all other variables are lengths. determine which formulas are dimensionally consistent.

Answer 1

Given that A is area, V is volume, and all other variables are lengths.

To get the dimensions of a quantity, it is easier to compare the unit of the quantity and represent each value in the unit by the dimension.

The formular that is dimensionally consistent is
$V= \frac{\pi d^3}{6}$