2026-09-10T00:15:06.936357 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL Write the formula \(V = \dfrac{4}{3}\pi r^{3}\) w...
Question 1 Report
Write the formula \(V = \dfrac{4}{3}\pi r^{3}\) with \(r\) as the subject.
This formula gives the volume of the sphere of radius \(r\) shown in the diagram. Show each step of your rearrangement.
Answer Details
The task is to isolate \(r\) in the sphere-volume formula. First remove the denominator by multiplying both sides by \(3\):
\[3V=4\pi r^3\quad\text{[M1]}\]
Then divide by \(4\pi\):
\[r^3=\frac{3V}{4\pi}\quad\text{[M1]}\]
Finally, take the cube root of both sides because \(r\) is cubed:
\[\boxed{r=\sqrt[3]{\frac{3V}{4\pi}}}\quad\text{[A1]}\]
A square root would not undo \(r^3\); the inverse operation required is a cube root.
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