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Sphere & Hemisphere Calculator

Compute radius, diameter, circumference, surface area, and volume of a sphere or hemisphere.

Sphere & hemisphere formulas

Surface areaSA = 4πr2
VolumeV = 43πr3
Hemisphere volumeV = 23πr3
Hemisphere total areaSA = 3πr2 (2πr2 curved + πr2 base)
Radius from volumer = ∛(3V4π)

Where r = radius

Worked examples

  1. A sphere has a radius of 3 cm. Find its surface area and volume.

    1. SA = 4π × 9 = 36π
    2. V = 43π × 27 = 36π

    Answer: SA ≈ 113.10 cm², V ≈ 113.10 cm³ (r = 3 is where the numbers match)

  2. A basketball has a circumference of 29.5 in. Find its volume.

    1. r = 29.52π ≈ 4.695 in
    2. V = 43π × 4.6953

    Answer: ≈ 433.5 in³

Tips & common mistakes

  • A sphere has the smallest surface area for a given volume — that is why bubbles are round.