lengthwise

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Diagram I

Diagram I shows a vessel in the shape of a prism.

The cross-section OAB is a sector of a circle of radius 8 cm and AÔB = 90°.

(a) (i) Calculate the perimeter of the sector OAB. [3]

(ii) The vessel, which stands on a horizontal table, contains 800cm3 of water, shown shaded in
the diagram.

Calculate the depth of the water in the vessel. [3]

(b)

O 20 O
8
8 x
Q
M N
A B
A B

P
Diagram II Diagram III

The vessel is now placed so that its curved surface is in contact with the horizontal table as shown
in Diagram II.

Diagram III shows the cross-section of the vessel with the shaded section representing the water.
P is the midpoint of the arc AB and is in contact with the table.
Q is the point on the water surface, MN, which is vertically above P.

It is given that OQ = x centimetres.

(i) (a) Write down an expression, in terms of x, for MN. [1]

(b) Show that the shaded area in Diagram III is (16π – x2) square centimetres. [2]

(ii) The vessel still contains 800 cm3 of water.

Given that the length of the vessel is 20 cm, find the value of x. [3]

© UCLES 2010 4024/21/M/J/10 [Turn over

 12

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a 488 cm
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No of cubes
Along width 3
5 11 6
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15 2 30 mber
2 layer
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4 The entrance to a zoo has this sign above it. Do not

write in this
margin
IF

B
A

H G

10

C D

F E

(a) The letter Z has rotational symmetry order 2 and DE is perpendicular to FE and CD.
CD = 35 cm, FE = 50 cm, DE = 10 cm and BC = 81 cm.
The perpendicular distance between BC and GF is 10 cm.

Calculate the area of the letter Z.

Answer ................................. cm2 [3]

© UCLES 2012 4024/21/M/J/12