The Student Room Group

C3 rate of change question OCR

Hi
I am stuck on one question in an OCR C3 textbook.
Exercise 9B, Q7
A funnel has a circular top of diameter 20cm and height 30cm.
When the depth of the liquid in the funnel is 15cm, the liquid is dripping from the funnel at the rate of 0.2 cm^3 per second. at what rate is the depth of the liquid in the funnel decreasing at this instant.
Basically, I did
dh/dt = dh/dV * dV/dt
work out dh/dV and use the dV/dt given but kept getting the wrong answer.
Where did I go wrong?

Thanks
Original post by TwinPrimes
Hi
I am stuck on one question in an OCR C3 textbook.
Exercise 9B, Q7
A funnel has a circular top of diameter 20cm and height 30cm.
When the depth of the liquid in the funnel is 15cm, the liquid is dripping from the funnel at the rate of 0.2 cm^3 per second. at what rate is the depth of the liquid in the funnel decreasing at this instant.
Basically, I did
dh/dt = dh/dV * dV/dt
work out dh/dV and use the dV/dt given but kept getting the wrong answer.
Where did I go wrong?

Thanks


Could you post your working please?
Reply 2
Original post by TwinPrimes
Hi
I am stuck on one question in an OCR C3 textbook.
Exercise 9B, Q7
A funnel has a circular top of diameter 20cm and height 30cm.
When the depth of the liquid in the funnel is 15cm, the liquid is dripping from the funnel at the rate of 0.2 cm^3 per second. at what rate is the depth of the liquid in the funnel decreasing at this instant.
Basically, I did
dh/dt = dh/dV * dV/dt
work out dh/dV and use the dV/dt given but kept getting the wrong answer.
Where did I go wrong?

Thanks


What did you put for dV/dt and dh/dV ?
Reply 3
I got V = 1/3 * pi * r^2 h
(h is the depth)
dV/dh = 1/3 * pi * r^2
so dh/dv = 3 / (pi * r^2)
dV/dt = 0.2 (given in the question)

I used r = 5cm, as the radius of the circular top of the funnel is 10cm, the depth of the liquid = 15 cm (ie 1/2 of the height of the funnel)
Plug everything in and it is not correct. the answer in the textbook is 0.0025. I got 0.007639

Sorry I really need to learn Latex

Quick Reply

Latest