Spheres: Volume and Surface Area

Geometry · Axiom Academy

LESSON Spheres: Volume and Surface Area The perfectly round 3D shape — and the two elegant formulas that measure it. Pick a center point and a distance r . The sphere is the set of all points in space exactly that far from the center. The radius is the one number that controls everything — its size, its volume, and its surface area. Both formulas are built from just the radius — one uses it cubed (a volume fills space, so it scales like length³) and one uses it squared (a surface is 2D, so it scales like length²). Volume — radius cubed, times 4/3, times π Surface area — four times the area of a circle The surface area of a sphere equals exactly 4 times the area of a circle with the same radius — its "great circle." It's also the same as the lateral surface of a cylinder with radius r and height 2r: the sphere fits perfectly inside that can. A basketball has a radius of 12 cm . Find its volume. (Use π ≈ 3.14.) 5. Example: Finding Surface Area A globe has diameter 16 inches . Find its surface area. (Use π ≈ 3.14.) 6. Example: Finding Radius from Volume A sphere has volume 904.32 m³ . Find its radius. (Use π ≈ 3.14.) Always divide by 2 first: r = d / 2, then use the formula. Surface area grows ×4 (r²), but volume grows ×8 (r³). You can now measure any sphere from a single number — its radius — using the two formulas and the great-circle relationship behind them. Scroll up to revisit any step.

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