SOLUTION: The formula for volume of a sphere is v=4/3pir^3 , where r is the radius of the sphere. Find the inverse of the function and explain what purpose v^-1 (x) serves.

Question 1016047: The formula for volume of a sphere is v=4/3pir^3 , where r is the radius of the sphere. Find the inverse of the function and explain what purpose v^-1 (x) serves.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
formula for volume of a sphere is v = 4/3 * pi * r^3.

solve this equation for r and you will get:

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

this means take (3/4 * 1/pi * v) and raise it to the 1/3 power.

this translates to take the cube root of (3/4 * 1/pi * v).

when you graph the original equation:

v = 4/3 * pi * r^3 becomes y = 4/3 * pi * x^3.

y is the volume
x is the radius

when you graph the inverse equation:

r = (3/4 * 1/pi * v)^(1/3) becomes y = (3/4 * 1/pi * v)^(1/3).

y is the radius
x is the volume.

the inverse function gets you back to the where you started from.

you use the original equation to solve for the volume, given the radius.
you use the inverse equation to solve for the radius, given the volume.

the graph of the original equation and the inverse equation is shown below:

$$$

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