2025 SCGS PRELIMS P1 Q1
2025 SCGS PRELIMS P1 Q1
Secondary 4
4 marks
Oil is dripping into an empty inverted right circular cone at the rate of \(16\ \mathrm{cm}^3\) per second.
At each instant, the oil forms a smaller similar cone. Its height, \(h\) cm, of the oil cone is three-quarters its radius, \(r\) cm.
[Volume of a right circular cone = \(\frac{1}{3} \times \pi \times r^2 \times h\)]
- Show that the volume, \(V\ \mathrm{cm}^3\), of oil is \(V = \frac{1}{4}\pi r^3\).[1]
- Calculate, at the instant when the radius is 8 cm, the rate of change of the radius of the oil surface.[3]
Video Solution:
Video solution locked
A free account saves your progress; this video needs a course plan.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs a course plan.
Create a free account to practise similar questions.
Answer:(a) \(V=\frac{1}{4}\pi r^3\) (b) \(\frac{\mathrm{d}r}{\mathrm{d}t}=\frac{1}{3\pi}\ \mathrm{cm\ s^{-1}}=0.106\ \mathrm{cm\ s^{-1}}\)
Need help? Join our A-Maths tuition classes.
Learn more