Express the radius r of a sphere as a function of the volume V it encloses.

v = 4/3 π r^3

through the magic of algebra...

r^3 = 3/4 v / π

take cube root of both sides

r = cube root of 3/4 v/pi

Well, if you're looking for a formula that relates the radius of a sphere to its volume, you're in luck! Assuming we're not clowning around with imaginary numbers here, the formula you're seeking is:

r = (3V/4π)^(1/3)

So, the radius (r) of a sphere is equal to the cube root of three times the volume (V), divided by four times the magical constant π. Why is it magical, you might ask? Well, it's irrational, meaning it doesn't make any sense! Just like trying to fit a clown car into a handbag.

To express the radius r of a sphere as a function of the volume V it encloses, we can use the formula for the volume of a sphere and rearrange the equation.

The formula for the volume of a sphere is given by:

V = 4/3 * π * r^3

To express the radius r as a function of the volume V, we can rearrange the equation as follows:

1) Start with the volume equation:
V = 4/3 * π * r^3

2) Divide both sides of the equation by (4/3 * π):
V / (4/3 * π) = r^3

3) Take the cube root of both sides of the equation to solve for r:
r = (V / (4/3 * π))^(1/3)

Therefore, the radius r of a sphere can be expressed as a function of the volume V it encloses as:

r = (V / (4/3 * π))^(1/3)

To express the radius of a sphere as a function of the volume it encloses, we need to use the formula for the volume of a sphere and then solve for the radius.

The formula for the volume of a sphere is:
V = (4/3) * π * r^3

To express the radius r as a function of the volume V, we'll follow these steps:

Step 1: Start with the volume formula.
V = (4/3) * π * r^3

Step 2: Isolate the variable r.
Divide both sides of the equation by (4/3) * π:
V / [(4/3) * π] = r^3

Step 3: Take the cube root of both sides.
r = cube root of (V / [(4/3) * π])

So, the expression for the radius r as a function of the volume V is:
r = (V / [(4/3) * π])^(1/3)

This equation allows you to find the radius of a sphere when you know its volume. Simply substitute the given volume value into the equation and calculate the result for the radius.