A solid sphere is cut into 6 equal wedges. The volume of each wedge is V = 2992 πr3. Solve the formula for r.

Question

V = 2992 πr³. Solve the formula for r.

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The volume V of a sphere is given by the formula V = 4/3 * πr³.

If a sphere is cut into 6 equal wedges, the volume of each wedge is 1/6 of the total volume of the sphere.

So, 1/6 * (4/3 * πr³) = 2992 πr³.

Solving this equation for r, we get:

4/3 * πr³ = 17952 πr³.

Divide both sides by πr³, we get:

4/3 = 17952.

Multiply both sides by 3/4, we get:

r³ = 13464.

Take the cube root of both sides, we get:

r = ∛13464.

So, r = 24.

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