GeoGebra

Cones - Overview

Author:
Christine
Topic:
Cone
Cone Facts: Notice these interesting things:
  • It has a flat base
  • It has one curved side
   
  • The pointy end of a cone is called the apex
  • The flat part is the base
  • An object shaped like a cone is said to be conical
Surface Area of a Cone: The Surface Area has two parts:
  • The Base Area = π × r2
  • The Side Area = π × r × s
Which together makes: Surface Area = π × r × (r + s) Note: we can calculate s = √(r2+h2) Example: h = 7 and r = 2 Surface Area of Base= π × r2      = π × 22       = 4π       ≈ 12.57   Surface Area of Side= π × r × √(r2+h2)       = π × 2 × √(22+72)       = π × 2 × √(4+49)       = 2π√(53)       ≈ 45.74 Total Surface Area ≈ 12.57 + 45.74 ≈ 58.31 Volume of a Cone: Volume = 1/3 π × r2 × h Example: h = 7 and r = 2 Volume= 13 π × r2 × h    = 13 π × 22 × 7    = 283 π    ≈ 29.32 Volume of a Cone vs Cylinder: The volume formulas for cones and cylinders are very similar:
The volume of a cylinder is:  π × r2 × h
The volume of a cone is:  1/3 π × r2 × h
So a cone's volume is exactly one third ( 13 ) of a cylinder's volume. Different Shaped Cones: Construction Cone This is almost a cone, but the top is chopped off (called a "truncated cone"). Also it has a wider base added so it doesn't fall over!

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