Geometry

16

16.1 Introduction

EMBCF

Geometry is a good subject for learning not justabout the mathematics of two and three-dimensional

shapes, but also about how we construct mathematical arguments. In thischapter you will learn how

to prove geometric theorems and discover someof the properties of shapes through small logicalsteps.

See introductory video:VMfqd at http://www.everythingmaths.co.za

16.2 Right Pyramids, Right Cones and Spheres

EMBCG

A pyramid is a geometric solid that has a polygon base and the base isjoined to a point, calledthe

apex. Two examples ofpyramids are shown inthe left-most and centrefigures in Figure 16.1. The

right-most figure has anapex which is joined toa circular base and thistype of geometric solidis

called a cone. Cones are similar to pyramids except that their bases arecircles instead of polygons.

Figure 16.1: Examples of a square pyramid, a triangular pyramid and a cone.

Surface Area of a Pyramid

The surface area of a pyramid is calculated by adding the area of each face together.

Example 1: Surface Area

QUESTION

If a cone has a heightof h and a base of radius r, show that the surfacearea is πr^2 +

πr

√

r^2 + h^2.