So far the machines run forward: measurements in, volume out. Exams love reverse: here's the volume — find the edge, the radius, the height. The rule is to undo each operation with its opposite, outermost first. A cube's edge got cubed, so a CUBE root brings it home: $a = \sqrt[3]{V}$ (read aloud: a equals the cube root of V). A sphere's radius hides under a 4/3, a π and a cube — peel the constants off first, then take the root: $r = \sqrt[3]{\tfrac{3V}{4\pi}}$.

Know which root you owe. A squared length (a circle floor) is undone by a SQUARE root; three multiplied lengths take the cube root. And roots always come LAST — divide every constant away before reaching for the radical, or the constants get rooted along with the radius and the answer lands in between everything sensible.