To determine if the given steps correctly solve for the radius \( r \) of a sphere from its volume formula, let's start with the volume formula itself:
\[ V = \frac{4}{3} \pi r^3 \]
To isolate \( r \), we need to reverse the operations correctly. Here are the steps broken down:
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Multiply both sides by 3: \[ 3V = 4 \pi r^3 \]
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Divide both sides by 4: \[ \frac{3V}{4} = \pi r^3 \]
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Divide both sides by \( \pi \): \[ \frac{3V}{4\pi} = r^3 \]
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At this step, to solve for \( r \), we need to take the cube root of both sides, which is not the same as simply dividing by 3: \[ r = \sqrt[3]{\frac{3V}{4\pi}} \]
Given this analysis, step 4 in your provided process is incorrect because it suggests dividing by 3 instead of taking the cube root.
Therefore, the correct response is:
False; steps 1 - 3 are correct, but step 4 does not give the inverse operation of \( r^3 \).