Question

The volume of a sphere may be found using the formula v=43πr3. What is the formula solved for r?

Answer 1

To solve the formula for the volume of a sphere for the radius r, one must multiply by 3/4, divide by π, and then take the cube root of the entire expression, resulting in r = ∛((3V)/(4π)).

Step-by-step explanation:

The volume of a sphere is given by the formula V = 4/3 πr³. To solve for the radius r, one would rearrange the formula as follows:

1. Multiply both sides of the equation by 3/4 to isolate πr³ on one side, resulting in (3/4)V = πr³.
2. Divide both sides by π to get (3/4)V/π = r³.
3. Take the cube root of both sides to solve for r, giving the result r = ∛((3/4)V/π).

So, the formula solved for r is r = ∛((3V)/(4π)).