©G Dear 2009 – Not to be sold/Free to use Spherical Geometry General Mathematics HSC Great Circles and Small Circles Stage 6 - Year 12 Press Ctrl-A ©G Dear 2009 – Not to be sold/Free to use

Any circle passing through the poles. Great Circles (1/4) Any circle passing through the poles. North Pole Great Circle (Equator) Axis South Pole

Length of Great Circles (2/4) Diameter Radius D 2r C = r = 20 cm C = 2xx20 ≈ 126 cm D = 20 cm C =  x 20 ≈ 62.8 cm Press

Any circle perpendicular to the axis. Small Circles (3/4) Any circle perpendicular to the axis. Axis A Series of Small Circles Press

Small Circles (4/4) C = 2  r = 2 x  x 5 = 31.4 cm To calculate the length of the small circle we need to know the length of its radius. r C = 2  r 5cm = 2 x  x 5 = 31.4 cm