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How will you solve for \[{r^2}:S = 4\pi {r^2}h\] ?
\[
A )\dfrac{{{S^2}}}{{4\pi h}} \\
B ) \dfrac{S}{{4\pi h}} \\
C ) \dfrac{S}{{4{\pi ^2}h}} \\
D ) \dfrac{{\sqrt S }}{{4\pi h}} \\
\]

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Last updated date: 19th Jul 2024
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Answer
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Hint:The key for solving this problem easily is to isolate \[{r^2}\]. The elimination method can be used for solving systems of linear equations and to solve the value for P. Here we can add the same value to each side of the equation while keeping the equation balanced.

Complete step by step solution:
Here while keeping the equation balanced we need to divide each side of the equation by \[4\pi h\] to solve for \[{r^2}\]
\[\dfrac{S}{{4\pi h}} = \dfrac{{4\pi {r^2}h}}{{4\pi h}}\]
While further simplifying the equation by cancelling the terms value of \[{r^2}\] is
\[\dfrac{S}{{4\pi h}} = {r^2}\]
So the value for \[{r^2}\] comes out to be \[\dfrac{S}{{4\pi h}}\] which means that the correct answer is option B.

Additional information: To solve this problem in a better way it is important to simplify each side of the equation by removing parentheses and combining like terms. Addition or subtraction is used to isolate variable terms on one side of the equation while to solve the variable multiplication or subtraction is used.

Notes: Remember the complete solution is the result of both the positive and negative portions of the solution. We can also further simplify the equation to solve for \[r\] by taking the square root of both sides of the equation for eliminating the exponent on the left side\[r = \sqrt {\dfrac{S}{{4\pi h}}} \]
Remember that the solution of the linear equation is not affected if the same number is added or subtracted from both sides of the equation and if both the sides of the equation are multiplied or divided by the same non-zero number.