Everything Maths Grade 10

SOLUTION

surface area of sphere= 4r^2

= 4(5)^2

= 100

=314,2 cm^2

Worked example 11: Examining the surface area of a cone

QUESTION

If a cone has a height ofhand a base of radiusr, show that the surface area is:r^2 +r

p

r^2 +h^2

SOLUTION

Step 1: Sketch and label the cone

r

h

a

r

h

Step 2: Identify the faces that make up the cone

The cone has two faces: the base and the walls. The base is a circle of radiusrand the walls can be opened
out to a sector of a circle:

2 r= circumference

a

This curved surface can be cut into many thin triangles with height close toa(whereais the slant height). The
area of these triangles or sectors can be summed as follows:

Area of sector=

1

2

baseheight (of a small triangle)

=

1

2

 2 ra

=ra

Chapter 13. Measurements 437