4400 Higher June 2006 Paper 3 Q10

EdexcelHigherOld spec9 marksCircles & Sectors

10

Circle with centre O and diameter 135 m; A at the bottom and C at the top of the vertical diameter; B on the circle next to A; lines OB and CB drawn

Diagram NOT accurately drawn

The diagram represents part of the London Eye.
\(A\), \(B\) and \(C\) are points on a circle, centre \(O\).
\(A\), \(B\) and \(C\) represent three capsules.
The capsules at \(A\) and \(B\) are next to each other.
\(A\) is at the bottom of the circle and \(C\) is at the top.

The London Eye has 32 equally spaced capsules on the circle.

(a) Show that angle \(AOB = 11.25^\circ\). (1)
(b) Find the size of the angle between \(BC\) and the horizontal. (3)

The capsules move in a circle of diameter 135 m.

(c) Calculate the distance moved by a capsule in making a complete revolution.
Give your answer correct to 3 significant figures. (2)

The capsules move at an average speed of 0.26 m/s.

(d) Calculate the time taken for a capsule to make a complete revolution.
Give your answer in minutes, correct to the nearest minute. (3)
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