Problem

18. Given the formula $V=\frac{4}{3} r^{2} h$, solve for $r$.

Solution

Step 1 :Given the formula \(V=\frac{4}{3} r^{2} h\), we are asked to solve for \(r\).

Step 2 :First, we isolate \(r^{2} h\) on one side of the equation by multiplying both sides by \(\frac{3}{4}\). This gives us \(r^{2} h = \frac{3}{4} V\).

Step 3 :Next, we isolate \(r^{2}\) by dividing both sides by \(h\). This gives us \(r^{2} = \frac{3}{4} \frac{V}{h}\).

Step 4 :Finally, we solve for \(r\) by taking the square root of both sides. This gives us \(r = \sqrt{\frac{3}{4} \frac{V}{h}}\).

Step 5 :Therefore, the solution for \(r\) is \(\boxed{r = \sqrt{\frac{3}{4} \frac{V}{h}}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/17572/

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