Geometry

Volume of a Sphere

Why V = (4/3)πr³

  • High school
  • about 3 min
  • 9 of 9 in the family
Not started
r=2
r = 2
V=43πr3=43π⋅23=33.510V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi\cdot2^3 = 33.510
A=4πr2=4π⋅22=50.265A = 4\pi r^2 = 4\pi\cdot2^2 = 50.265

Volume of a sphere = integral of circular cross-sections. Each cross-section at height y has area π(r²-y²) – integrated, this gives 4πr³/3. Cavalieri's principle.