Cambridge International Mathematics

Mensuration (solids and containers) (Chapter 11) 235

9 A squash court has the dimensions given. Each shot

may strike the floor, or the walls below the red line

and excluding the board on the front wall. Calculate

the total surface playing area of the walls and the floor.

SOLIDS WITH CURVED SURFACES

Cylinders

So, for a hollow cylinder, the outer surface area A=area of rectangle

) A=length£width

) A=2¼r£h

) A=2¼rh

Object Figure Outer surface area

Hollow cylinder A=2¼rh (no ends)

Hollow can A=2¼rh+¼r^2 (one end)

Solid cylinder A=2¼rh+2¼r^2 (two ends)

board

6.4 m

9.75 m

50 cm

4.6 m

2.1 m

r

h

open out flattened surface area

r

cut here

h

h

2 pr

hollow 2 pr

r

h

hollow

hollow

r

h

hollow

solid

r

h

solid

solid

Consider the cylinder shown alongside. If the cylinder is cut, opened out and

flattened onto a plane, it takes the shape of a rectangle.

We will consider the outer surface area of three types of object with curved

surfaces. These arecylinders cones, andspheres.

You can verify that the curved surface produces a rectangle by peeling the label off a cylindrical can and

noticing the shape when the label is flattened. The length of the rectangle is the same as the circumference

of the cylinder.

Give your answer correct to 4 significant figures.

IGCSE01

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Y:\HAESE\IGCSE01\IG01_11\235IGCSE01_11.CDR Friday, 3 October 2008 4:31:46 PM PETER