Question

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

Answer 1

The given formula is

`V=(2)/(15)\pi r^3`

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

`\begin{gathered} 15V=15\cdot(2)/(15)\pi r^3 \\ 15V=2\pi r^3 \end{gathered}`

Now, we divide the equation by 2pi

`\begin{gathered} (15V)/(2\pi)=(2\pi r^3)/(2\pi) \\ (15V)/(2\pi)=r^3 \end{gathered}`

Then, we take the cubic root on both sides

`\begin{gathered} \sqrt[3]{(15V)/(2\pi)}=\sqrt[3]{r^3} \\ \sqrt[3]{(15V)/(2\pi)}=r \end{gathered}`

Therefore, the formula solved for r is

`r=\sqrt[3]{(15V)/(2\pi)}`