A Level maths past paper question help needed

Can anyone explain to me whats going on with question 13?
I've looked at the MS too but still don't really get it, especially where the first line of the MS comes from...
Paper: https://hgsmaths.com/year-13/maths/p...paper-1-qp.pdf
MS: https://hgsmaths.com/year-13/maths/p...paper-1-ms.pdf

Reply 1

cloudii

Can you send a screenshot, I don't think the link is working.

Reply 2

h6yates

Original post by cloudii

Can you send a screenshot, I don't think the link is working.

Oh not sure why that is, here Screenshot 2023-06-04 180822.png

Reply 3

cloudii

Original post by h6yates

Oh not sure why that is, here Screenshot 2023-06-04 180822.png

Okay, so this is just a differential equations question. In the question it tells you that water is leaking out of the bottom of the container, so this would be our rate of change of the volume (or dV/dt - they've made it negative as the volume is decreasing). For the ratio with r and h, they've used similar triangles, so essentially saying that the ratio r/h is equivalent to the ratio 2.5/4. When these questions give you something like the volume of a cone, you'd usually want to try and set up some sort of chain rule equation, as they've done in the fourth line of the mark scheme, so using the volume equation you can differentiate with respect to h. You can then link your differential equations, your dV/dh and your dV/dt, so you'd need to use dh/dt in order for things to cancel out. The rest is just substituting in your values and rearranging as required. Let me know if you need more detail :smile: