Answered

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A solid sphere is cut into 10 equal wedges. The volume of each wedge is V = ²/15*pi*r³Solve the formula for r.

Sagot :

The given formula is

[tex]V=\frac{2}{15}\pi r^3[/tex]

To solve for r, first, we need to multiply the equation by 15

[tex]\begin{gathered} 15V=15\cdot\frac{2}{15}\pi r^3 \\ 15V=2\pi r^3 \end{gathered}[/tex]

Now, we divide the equation by 2pi

[tex]\begin{gathered} \frac{15V}{2\pi}=\frac{2\pi r^3}{2\pi} \\ \frac{15V}{2\pi}=r^3 \end{gathered}[/tex]

Then, we take the cubic root on both sides

[tex]\begin{gathered} \sqrt[3]{\frac{15V}{2\pi}}=\sqrt[3]{r^3} \\ \sqrt[3]{\frac{15V}{2\pi}}=r \end{gathered}[/tex]

Therefore, the formula solved for r is

[tex]r=\sqrt[3]{\frac{15V}{2\pi}}[/tex]

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