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

Question

asked Aug 17, 2021 74.1k views

1 Answer

Ranjan Sarma · Answer 1 · 2021-08-21T22:18:09+0000

Answer:

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

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

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