Spheres & Cross Sections

Hanna Ingham, Apr 19, 2018


  • 1. Surface Area of Spheres with Proof
  • 2. Illustration of surface area of a sphere
  • 3. Sections of Spheres
  • 4. Curved Surface Area of Cones (Parametric Curved Surface)
  • 5. Pyramid section
  • 6. Cross Section Pyramid

1.

Surface Area of Spheres with Proof

Drag the red point to see how a sphere can be dissected into n pyramids (approximate) of heights equal the radius r.[br]Let A1, A2, ..., An be the base areas of the pyramids.[br](a) Show that 1/3 (A1+ A2 + ... + An) r ≈ Volume of the sphere[br](a) When n tends to infinity, show that [br] 1/3 S r = V[br] where V and S are the volume and surface area of the sphere respectively. [br] Hence show that[br] S = 4 π r² .
– Anthony OR 柯志明

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