Page 12 - 1202 Question Bank Additional Mathematics Form 5

Section B
[16 marks]
Answer any two questions from this section.

13. (a) A rectangular container without a lid is made up of thin aluminium sheet. The sides of the base are 2x cm and
3x cm and the height is h cm. If the total surface area is 200 cm ,
2
20
3x
(i) show that h = —– – —–, [2 marks]
x
5
(ii) find the dimensions of the container such that the volume is maximum,
[2 marks]
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(iii) hence, find the maximum volume of the container.
[1 mark]
(b) If water drips into the container in (a) at a constant rate of 21 cm s , find the rate of change of the height of water
–1
3
in the container when h = 1 cm.
[3 marks]
Answer:
(a) (i)

(ii)

(iii)

(b)

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09_1202 QB AMath F5.indd 87 04/12/2021 9:25 AM