Geometry and Trigonometry practice question

Answer: B. 36π

V = (4/3)π(3³) = (4/3)π(27) = 36π. Choice C (108π) forgets to divide by 3 (it uses 4πr³); the sphere volume formula includes the 1/3 factor.

Why the other answers are wrong

A. 12π

You squared the radius instead of cubing it: (4/3)π(9) = 12π. With 3³ = 27, you get (4/3)π(27) = 36π.

C. 108π

108π is 4π(3³) — you dropped the 1/3 in the formula. Dividing 4π(27) by 3 gives 36π.

D. 324π

324π doesn't come from a single slip in the formula; it's 4π(81), using a fourth power and no 1/3. Work it straight through: 3³ = 27, then (4/3)(27) = 36, so V = 36π.

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