Question 1064469
v = 4/3 * pi * r^3


solve for r in radical form.


start with v = 4/3 * pi * r^3
divide both sides of the equation by (4/3 * pi) to get:
v/(4/3 * pi) = r^3
this can be simplified to (3v/4 * pi) = r^3
take the third root of each side of the equation to get:


r = {{{root(3,3v/(4*pi)))}}}


solve for r in exponent form.


same process except the result is shown as:


r = {{{(3v/(4*pi))^(1/3)}}}


last question:


v = 256π/3


solve for r.


r should be equal to {{{(((3 * 256 * pi / 3)) / (4 * pi)) ^ (1/3)}}}


that would make r equal to 4.


to see if this is correct, go back to the volume formula of v = 4/3 * pi * r^3


that formula becomes v = 4/3 * pi * 4^3 which becomes v = 4/3 * pi * 64 which becomes v = 256 * pi / 3.


this is the same as v = 256pi/3 which is where we started from, so the solution looks good.


i used pi instead of the symbol for pi that you showed.
pi means the same thing as π


it's not as formal, but it's a lot quicker to do it that way.


works fine unless you're required to use the proper mathematical symbol.