Question

Solve for r. v=4/3πr³ what is r equal to?(Hint: Notice that r is cubed, not squared.)

A. r=∛V/43π
B. r=V/43π
C. r=∛V/43π
D. r=∛V / 43π

Answer 1

The solution to the equation v=4/3πr³ for r is to multiply by 3/4, divide by π, and take the cube root, resulting in the answer r=∓V/(4π/3), which corresponds to option D.

Step-by-step explanation:

To solve for r in the equation v=4/3πr³, we need to isolate r on one side of the equation. This involves a few algebraic steps. Here's how you do it step by step:

1. Multiply both sides of the equation by 3/4 to cancel out the 4/3 on the right side: 3/4 × v = πr³.
2. Divide both sides by π to isolate r³: (3/4 × v) / π = r³.
3. Take the cube root of both sides to solve for r: r = √((3/4 × v) / π).

Now, in simplified notation, that cube root of v divided by 4/3π will actually look like r=√V/((4/3)π), or with the cube root sign, r=∓(V/(4/3π)).

The correct answer is therefore D. r=∓V/(4π/3).