Answer:
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" r = [tex]( \frac{a}{4 \pi })^ \frac{1}{2} [/tex] " ;
or; write as: " r = [tex] \sqrt{ \frac{a}{4 \pi } } [/tex] " ;
or; write as: " r = [tex] \frac{ \sqrt{a} }{ \sqrt{4 \pi } } [/tex] " .
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Explanation:
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Note the formula for the surface area, "a" ; of a sphere:
→ " a = 4 π r² " ;
→ Let us rearrange the equation to isolate "r" on one side of the equation:
→ Given: " a = 4 π r² " ;
↔ 4 π r² = a ;
Divide EACH side of the equation by " [4 * π] " ;
→ {4 π r²} / [4 * π] = a / [4 * π] ;
to get:
→ r² = { [tex] \frac{a}{4 \pi } [/tex] } ;
Now, take the POSITIVE square root of each side of the equation;
to isolate "r" on one side of the equation;
→ √(r²) = √ { [tex] \frac{a}{4 \pi } [/tex] } ;
→ " r = [tex]( \frac{a}{4 \pi })^ \frac{1}{2} [/tex] " ;
or; write as: " r = [tex] \sqrt{ \frac{a}{4 \pi } } [/tex] " ;
or; write as: " r = [tex] \frac{ \sqrt{a} }{ \sqrt{4 \pi } } [/tex] " .
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