Question

Solve for r in the equation V = 43πr³.

a) r = (V / (43π))^(1/3)
b) r = (V / (43π))^(1/2)
c) r = V / (43π)
d) r = (43π / V)^(1/3)

Answer 1

To solve for r in the equation V = 4/3πr³, you multiply by 3/4, divide by π, and take the cube root, resulting in r = (V / (4/3π))^(1/3). Option A is correct.

Step-by-step explanation:

The question involves solving for the variable r in the equation V = 4/3πr³, which describes the volume of a sphere. To isolate r, we need to perform a series of algebraic steps. First, multiply both sides by 3/4 to get rid of the fraction next to π and r³. Then divide by π to leave r³ on one side of the equation. Finally, take the cube root to solve for r.

Here is the step by step process:

Multiply both sides by 3/4: 3/4 * V = (3/4) * (4/3)πr³

Simplify: V = πr³

Divide both sides by π: V/π = r³

Take the cube root of both sides: r = (V/π)^(1/3)

Thus, the solution for r in the given equation is r = (V / (4/3π))^(1/3), which corresponds to option a).