Cambridge International Mathematics

252 Mensuration (solids and containers) (Chapter 11)

9 A cylindrical container with radius 12 cm is partly filled with water.

Two spheres with radii 3 cm and 4 cm are dropped into the water

and are fully submerged. Find theexactincrease in height of water

in the cylinder.

Discovery 1 Making cylindrical bins#endboxedheading

Your business has won a contract to make40 000cylindrical bins, each to contain 201 m^3.

To minimise costs (and therefore maximise profits) you need to design the bin of minimum surface area.

1 Find the formula for the volumeV and the outer surface areaAin

terms of the base radiusxand the heighth.

2 Convert 201 m^3 into cm^3.

3 Show that the surface area can be written as

A=¼x^2 +

100 000

x

cm^2.

4 Use thegraphing packageor agraphics calculatorto obtain a sketch of the function

Y=¼X^2 + 100 000=X

Find the minimum value ofY and the value ofXwhen this occurs.

5 Draw the bin made from a minimum amount of material. Make sure you fully label

your diagram.

6 Investigate the dimensions of a cylindrical can which is to hold exactly 500 ml of soft drink. Your

task is to minimise the surface area of material required. Remember your container will need two

ends.

Discovery 2 Constructing a lampshade

#endboxedheading

Click on the icon to obtain a printable copy of instructions on how to make a lampshade

which is of truncated cone shape.

Discovery 3 The turkey problem#endboxedheading

Click on the icon to obtain a printable copy of instructions on minimising materials needed

to fence an enclosure needed to keep turkeys.

GRAPHING

PACKAGE

LAMPSHADE

TURKEY

PROBLEM

no top

h

2 x

water

12 cm

What to do:

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
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100 100
Y:\HAESE\IGCSE01\IG01_11\252IGCSE01_11.CDR Friday, 31 October 2008 9:52:53 AM PETER