SOLUTION: The equation for the volume of a sphere is given to me but i have to find the radius and i dont know how to decompose radius to the 3rd power

Algebra ->  Square-cubic-other-roots -> SOLUTION: The equation for the volume of a sphere is given to me but i have to find the radius and i dont know how to decompose radius to the 3rd power       Log On


   

Question 976268: The equation for the volume of a sphere is given to me but i have to find the radius and i dont know how to decompose radius to the 3rd power
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
v=%284%2F3%29pi%2Ar%5E3, and you want to solve for a formula for r.

You must already know about multiplicative inverse.

v%283%2F4%29%281%2Fpi%29=r%5E3

and Symmetric Property of Equality:
r%5E3=v%283%2F4%29%281%2Fpi%29
and you want to know what to do to undo the exponent of 3.

Are you familiar or know some rules or laws about exponents?
Think this way:
r%2Ar%2Ar=r%5E3
-
Starting with r^3, you want the number which must be raised to exponent 3 to give r^3, which is r.
.

which is r%5E3.
.
More simply root%283%2Cr%5E3%29=r.

Can you conclude the next step or two in the formula, almost finished?


--
From here, r%5E3=v%283%2F4%29%281%2Fpi%29

Take cubed root of both sides.

root%283%2Cr%5E3%29=root%283%2Cv%283%2F4%29%281%2Fpi%29%29

r=root%283%2Cv%283%2F4%29%281%2Fpi%29%29
and with miner simplifying of the rational expression inside the cubed root,
highlight%28r=root%283%2C%28%283v%29%2F%284pi%29%29%29%29