Example 1
Completion requirements
| Example 1 |
The formula for the volume of a sphere is \(V = \frac{4}{3}\pi r^3 \). Rearrange the formula to solve for \(r\).
Step 1: Isolate \(r^3\).
\(\begin{align}
V &= \frac{4}{3}\pi r^3 \\
3V &= 4\pi r^3 \\
\frac{{3V}}{{4\pi }} &= r^3 \\
\end{align}\)
Step 2: Take the cube root of each side.
\(\begin{align}
\frac{{3V}}{{4\pi }} &= r^3 \\
\sqrt[3]{{\frac{{3V}}{{4\pi }}}} &= \sqrt[3]{{r^3 }} \\
\sqrt[3]{{\frac{{3V}}{{4\pi }}}} &= r \\
\end{align}\)
\(\begin{align}
V &= \frac{4}{3}\pi r^3 \\
3V &= 4\pi r^3 \\
\frac{{3V}}{{4\pi }} &= r^3 \\
\end{align}\)
Step 2: Take the cube root of each side.
\(\begin{align}
\frac{{3V}}{{4\pi }} &= r^3 \\
\sqrt[3]{{\frac{{3V}}{{4\pi }}}} &= \sqrt[3]{{r^3 }} \\
\sqrt[3]{{\frac{{3V}}{{4\pi }}}} &= r \\
\end{align}\)