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