Cambridge International Mathematics

236 Mensuration (solids and containers) (Chapter 11)

Cones

The curved surface of a cone is made from a sector of a circle with radius equal to the slant height of the

cone. The circumference of the base equals the arc length of the sector.

arc AB=

μ

μ

360

¶

2 ¼l

But arc AB=2¼r

)

μ

μ

360

¶

2 ¼l=2¼r

)

μ

360

=

r

l

The area of curved surface=area of sector

=

μ

μ

360

¶

¼l^2

=

³r

l

́

¼l^2

=¼rl

The area of the base=¼r^2

) the total area=¼rl+¼r^2

Object Figure Outer surface area

Hollow cone A=¼rl (no base)

Solid cone A=¼rl+¼r^2 (solid)

Spheres

Surface area A=4¼r^2

The mathematics required to prove this formula is beyond the scope of this course.

cut

r

l

2 pr

r

l

B

A

q°

r

l

r

l

r

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y:\HAESE\IGCSE01\IG01_11\236IGCSE01_11.CDR Thursday, 25 September 2008 12:19:42 PM PETER