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Dmitry_Shevchenko [17]
3 years ago
6

What is the radius of a sphere with a volume of 1/6 pie

Mathematics
1 answer:
Yakvenalex [24]3 years ago
3 0

Answer:

\large\boxed{the\ radius\ R=\dfrac{1}{2}}

Step-by-step explanation:

The formula of a volume of a sphere:

V=\dfrac{4}{3}\pi R^3

We have

V=\dfrac{1}{6}\pi

Substitute:

\dfrac{4}{3}\pi R^3=\dfrac{1}{6}\pi        <em>divide both sides by π</em>

\dfrac{4}{3}R^3=\dfrac{1}{6}          <em>multiply both sides by 3</em>

3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}R^3=3\!\!\!\!\diagup^1\cdot\dfrac{1}{6\!\!\!\!\diagup_2}

4R^3=\dfrac{1}{2}          <em>divide both sides by 4</em>

R^3=\dfrac{1}{2}:4\\\\R^3=\dfrac{1}{2}\cdot\dfrac{1}{4}\\\\R^3=\dfrac{1}{8}\to R=\sqrt[3]{\dfrac{1}{8}}\\\\R=\dfrac{\sqrt1}{\sqrt8}\\\\R=\dfrac{1}{2}

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