Answer:
D. [tex] r = \sqrt[3]{\frac{15V}{2\pi}} [/tex]
Step-by-step explanation:
Given:
Volume of each wedge, [tex] V = \frac{2}{15}\pi r^3 [/tex],
Required:
Solve for r (i.e. make r the subject of the formula)
SOLUTION:
[tex] V = \frac{2}{15}\pi r^3 [/tex]
Multiply both sides by 15
[tex] 15*V = 15*\frac{2}{15}\pi r^3 [/tex]
[tex] 15V = 2\pi r^3 [/tex]
Rewrite the equation
[tex] 2\pi r^3 = 15V [/tex]
Divide both sides by 2π
[tex] \frac{2\pi r^3}{2\pi} = \frac{15V}{2\pi} [/tex]
[tex] r^3 = \frac{15V}{2\pi} [/tex]
Take the cube root of both sides
[tex] \sqrt[3]{r^3} = \sqrt[3]{\frac{15V}{2\pi}} [/tex]
[tex] r = \sqrt[3]{\frac{15V}{2\pi}} [/tex]
