c4 maths chapter 4

Hi guys,
I can't seem to be able to do exercise 4E question 11. For those who dont have the book, the question is:

An inverted conical flask is full of salt. The salt is allowed to leave by a small hole in the vertex. It leaves at a constant rate of 6 cm^3/s.
Given that the angle of the cone between the slanting edge and the vertical i 30 degrees, show that the volume of the salt is (pi)h^3/9, where h is the height of salt at time t seconds.
Show that the rate of change of the height of the salt in the funnel is inversely proportional to h^2. Write down the differential equation relating h and t.

Thanks a lot for your help!

Reply 1

Trangulor

6

What bit are you stuck on? Finding the volume of the water left? Its just volume of a cone with the base written in terms of the height using the angle given.

For rate of change, you know that dV/dt is -6 (6 cubic centimetres leave per second). Substitute your equation for V (the volume) into that, differentiate implicitly and then rearrange to get dh/dt on one side

Reply 2

steve2005

17

universitybound

Hi guys,
I can't seem to be able to do exercise 4E question 11. For those who dont have the book, the question is:

An inverted conical flask is full of salt. The salt is allowed to leave by a small hole in the vertex. It leaves at a constant rate of 6 cm^3/s.
Given that the angle of the cone between the slanting edge and the vertical i 30 degrees, show that the volume of the salt is (pi)h^3/9, where h is the height of salt at time t seconds.

Here is first part

Picture 66.png12.3KB

Reply 3

steve2005

17

universitybound

Hi guys,
Show that the rate of change of the height of the salt in the funnel is inversely proportional to h^2. Write down the differential equation relating h and t.
!

I'm not sure what is required for the last part.

Picture 67.png39.3KB

c4 maths chapter 4

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