2025 PHS PRELIMS P1 Q7

2025 PHS PRELIMS P1 Q7

Secondary 4
7 marks
2025 Presbyterian High School Prelims A Math Paper 1

Peter constructed an open fish tank with a rectangular base of length \(4l\text{ m}\), breadth \(l\text{ m}\), and height \(h\text{ m}\). He wanted the total outer surface area of the fish tank to be \(5\text{ m}^2\).

  1. Show that the volume of the tank, \(V\text{ m}^3\), is given by \(V = \frac{2}{5}(5l - 4l^3)\).[3]
  2. Determine the area of the rectangular base for the tank to contain the maximum amount of water when filled to the brim.[4]

Solution:

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Answer:(a) \(V=\dfrac{2}{5}(5l-4l^3)\) (b) \(\dfrac{5}{3}\text{ m}^2\) or \(1.67\text{ m}^2\)

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