Everything Maths Grade 11

16.2 CHAPTER 16. GEOMETRY

SOLUTION

Step 1 : Draw a picture

r

h

r

a h

Step 2 : Identify the faces thatmake up the cone

The cone has two faces:the base and the walls.The base is a circle of radius r

and the walls can be opened out to a sector of acircle.

a

2 πr = circumference

This curved surface canbe cut into many thin triangles with height closeto a (a is

called the slant height). The area of these triangles will add up to^12 ×base×height(of

a small triangle) which is^12 × 2 πr× a = πra

Step 3 : Calculate a

a can be calculated by using the Theorem of Pythagoras. Therefore:

a =

�

r^2 + h^2

Step 4 : Calculate the area of the circular base

Ab= πr^2

Step 5 : Calculate the area of the curved walls

Aw = πra

= πr

�

r^2 + h^2

Step 6 : Calculate surface area A

A = Ab+ Aw

= πr^2 + πr

�

r^2 + h^2