658 Multi-Topic Questions (Chapter 33)i Write down a formula for the volume of this pyramid in terms ofx.
ii When the volume is numerically equal to the perimeter of the rectangular base, show that
2 x^2 +4x¡3=0.
iii Solve the equation 2 x^2 +4x¡3=0, giving your answers correct to 2 decimal places.
iv Use your answer toiiito write down the length of RS.
v M is the midpoint of ST. Calculate angle PMO.23 May 2002, Paper 4A sphere, centre C, rests on horizontal ground at A and touches a vertical wall at D. A straight plank
of wood, GBW, touches the sphere at B, rests on the ground at G and against the wall at W. The wall
and the ground meet at X. Angle WGX=42o.
a Find the values ofa,b,c,dandemarked on the diagram.
b Write down one word which completes the following sentence.
‘Angle CGA is 21 obecause triangle GBC and triangle GAC are .......’
c The radius of the sphere is 54 cm.
i Calculate the distance GA. Show all your working.
ii Show that GX= 195cm correct to the nearest centimetre.
iii Calculate the length of the plank GW.
iv Find the distance BW.24
The diagram shows a window ABCDE. ABDE is a rectangle.
BCD is an arc of a circle with centre O and radiusxcm.
The total height of the window is 90 cm. AB=ED=80cm
and AE=BD=40cm. The line OC is perpendicular to
BD, and BF=FD.
aiWrite down, in terms ofx, the length of OC and the
length of OF.
ii Use Pythagoras’ Theorem in triangle OFD to write
down an equation inx.
iii By solving the equation, show that x=25.
b Using a scale of 1 cm to represent 10 cm, construct an
accurate drawing of the window.
c Find the area of the window.
d The window is made of glass 2 mm thick. The mass of 1 cm^3 of the glass is 6 : 5 grams.
Calculate the mass of glass in the window, giving your answer in kilograms.42°b°a°e°c° d°GAXWDBCOB DAECF40 cm90 cm 80 cmxcm xcmAdapted from May/June 2000, Paper 4IGCSE01
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Y:\HAESE\IGCSE01\IG01_33\658IGCSE01_33.CDR Friday, 14 November 2008 10:33:21 AM PETER