Question

A solid sphere is cut into 4 equal wedges. The volume of each wedge is V = (1)/(3) π r³. Solve the formula for r.

Answer 1

To find the radius (r) from the volume (V) of a quarter sphere wedge where V = (1/3) π r^3, you multiply both sides by 3, divide by π, and then take the cube root of the result to isolate r.

Step-by-step explanation:

To solve the formula for the radius (r) given the volume (V) of a sphere wedge where V = (1/3) π r^3, we would need to isolate r. Here are the steps to do so:

1. Multiply both sides of the equation by 3 to get rid of the fraction: 3V = π r^3.
2. Divide both sides by π to solve for r^3: (3V) / π = r^3.
3. Take the cube root of both sides to find r: r = ∛((3V) / π).

The correct formula for the volume of a sphere is V = 4/3 (π) (r)^3, so when a sphere is cut into 4 equal wedges, each wedge has a volume of V = 1/4 the total sphere volume, which aligns with the given equation.