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Volume formula for a sphere

Aviation Mechanic General (AMG) practice question 13 of 25 on Mathematics. ACS element AM.I.H.K2 · difficulty: recall. Want to answer it in a timed quiz? Use the Aviation Mechanic General (AMG) practice mode.

Question bank updated 2026-09-22

QUESTIONThe volume of a sphere with radius r is given by the formula

  1. A4/3 × π × r³
  2. B4 × π × r²
  3. C1/3 × π × r² × h
Show the answer and explanation

Correct answer: A. 4/3 × π × r³

  • A — correct The handbook states the volume of a sphere as v = 4/3 × π × radius³, or equivalently 1/6 × π × d³.
  • B — incorrect This is the surface area of a sphere, not its volume.
  • C — incorrect This is the volume formula for a cone, which has a height term; a sphere has no height dimension in its formula.

BACKGROUND

A sphere is a solid having the shape of a ball, with a constant diameter. Its radius is one-half of its diameter. The handbook gives the volume as v = 4/3 × π × r³, or v = 1/6 × π × d³ using the diameter. Volume is expressed in cubic units, such as cubic inches or cubic feet. The surface area of a sphere is a different quantity, 4 × π × r².

STUDY TIP

Keep volume formulas (cubic units, radius cubed) separate from surface-area formulas (square units, radius squared).

KEY POINTS

  • Sphere volume = 4/3 × π × r³ (or 1/6 × π × d³).
  • Sphere surface area = 4 × π × r².
  • Cone volume = 1/3 × π × r² × h.

SOURCES

  • FAA-H-8083-30B ch03 "Sphere" (Computing Volume of Three-Dimensional Solids)
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SkyDrill is not affiliated with the FAA. This is an original practice item based on FAA-H-8083-30B Aviation Maintenance Technician Handbook – General, 14 CFR part 43 and part 65. Regulations and handbooks are revised; confirm details against the current edition.