Differentiation - Connected Rates of Change
Differentiation - Connected Rates of Change
A container in the shape of a hemi-sphere of radius \(8\) cm is completely filled with water. The water is then poured into an empty inverted right circular cone of radius \(8\) cm and height \(16\) cm at a steady rate.
- Given that all the water is poured in \(5\frac{1}{3}\) minutes and that \(V\) cm\(^3\) represents the amount of water in the cone at any time, \(t\) show that \(\dfrac{\mathrm{d}V}{\mathrm{d}t}=64\pi\) cm\(^3\)/min.
- Leaving your answers in terms of \(\pi\),
- Express the volume of water in the cone in terms of \(h\), where \(h\) is the depth of water in the cone.
- Find the rate of change of the height of water level in the circular cone, when the height of the water level in the cone is \(6\) cm.
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) \(64\pi\text{ cm}^3\text{ min}^{-1}\) (b)(i) \(V=\frac{\pi h^3}{12}\text{ cm}^3\) (b)(ii) \(\frac{\mathrm dh}{\mathrm dt}=\frac{64}{9}\text{ cm min}^{-1}\)
Need help? Join our A-Maths tuition classes.
Learn more