SOLUTION: A) The formula for the volume of a sphere of radius r is V(r) = 4/3πr^3. Solve this equation for r. Write two versions, one in radical form and one in exponential form. B)

Algebra ->  Volume -> SOLUTION: A) The formula for the volume of a sphere of radius r is V(r) = 4/3πr^3. Solve this equation for r. Write two versions, one in radical form and one in exponential form. B)      Log On


   

Question 1064469: A) The formula for the volume of a sphere of radius r is V(r) = 4/3πr^3. Solve this equation for r. Write two versions, one in radical form and one in exponential form.
B) Determine the radius of a sphere with a volume of 256π/3 m^3
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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%283%2C3v%2F%284%2Api%29%29%29

solve for r in exponent form.

same process except the result is shown as:

r = %283v%2F%284%2Api%29%29%5E%281%2F3%29

last question:

v = 256π/3

solve for r.

r should be equal to %28%28%283+%2A+256+%2A+pi+%2F+3%29%29+%2F+%284+%2A+pi%29%29+%5E+%281%2F3%29

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.