## Solve for \(V=\frac{1}{3} \pi r^{2} h ?\)

Answer:

Move terms that don’t have h in them to the other side (using addition/subtraction), then move all factors other than h to the other side (using multiplication/division).

Explanation:

If we want to solve \(V=\frac{1}{3} \pi r^{2} h\) for \(h\), we need to isolate the term with \(h\) (already done), and then multiply both sides by the inverses of everything other than \(h\).

The multiplication by \(\frac{3}{\pi r^{2}}\) to both sides is our choice; we do this so that each piece other than \(h\) has a multiplicative inverse that cancels it off.

Thus, our cone volume formula, when solved for \(h\), is

\(h=\frac{3 V}{\pi r^{2}}\)