Question

A solid sphere is cut into 10 equal wedges. The volume of each wedge is V=2/15pi r^3

Solve the formula for r

I’m really confused sorry please help

Answer 1

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

Explanation:

Given:

Volume of each wedge,
`V = (2)/(15)\pi r^3`,

Required:

Solve for r (i.e. make r the subject of the formula)

SOLUTION:

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

Multiply both sides by 15

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

`15V = 2\pi r^3`

Rewrite the equation

`2\pi r^3 = 15V`

Divide both sides by 2π

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

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

Take the cube root of both sides

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

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