2025 JVSS PRELIMS P1 Q6

2025 JVSS PRELIMS P1 Q6

Secondary 4
6 marks
2025 Jurongville Secondary School Prelims A Math Paper 1

A balloon is being inflated such that its volume increases and the radius, \(r\) cm of the balloon, changes over time.

The rate of change of the radius at time \(t\) seconds is given by \(\frac{dr}{dt}=\frac{4}{t+2},\ t>0\).

Initially, at \(t=0\), the radius is 3 cm.

  1. Find an expression for \(r\) in terms of \(t\).[2]
  2. The volume \(V\) of the balloon is given by \(V=\frac{4}{3}\pi r^3\).[4]
    Find the rate of increase of the volume of the balloon at \(t=2\).

Solution:

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Answer:\((a)\) \(r=3+4\ln\left(\frac{t+2}{2}\right)\) \((b)\) \(419\text{ cm}^3\text{/s}\)

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