Maths differential equation question

Hi,
Please could I have some help on this question? I’ve attached my working.
https://ibb.co/S7vg2LyB
https://ibb.co/DfJHqpy0
Thanks!

The radius changes with time, but its proportional to h (similar triangles). So
V(t) ~ h(t)^3

I never stand what you mean by the radius changing with time and it is proportional to h but I don’t get how you have represented it sorry

The volume of the water cone at time t is given by
V(t) = pi/3 r(t)^2 h(t)
Both the height of the water cone h and the base radius of the water cone r are functions of time.
If you double the height, youll double the base radius (similar triangles) so
r(t) = k h(t)
for some k, but you could do simple trig and note its tan(theta), where theta is half the angle at the apex of the cone (so create a right triangle).

Actually sorry I was looking over it but I’m confused about r(t) = kh(t) does the t bracket mean functions are varying with time and can I candel the t out so I can sub it into the volume equation?

Its just being explicit that they are functions of time. So r(t) means the radius is a function of time, just as h(t) is. In your original working you had
V = pi/3 r^2 h
but seemed to treat the base radius as constant and it bore no relation to the height when you differentiated and its easy to make "errors" like this. Usually the (t) is suppressed/inferred, as necessary, so V(t), h(t), ... are just written as V, h, ... but you differentiate them wrt t etc so they must be functions of time.
But as long as you understood this
V = pi/3 k^2 h^3 = m h^3
and go with that ... though pi/3 k^2 is just another constant m.

ohh yes ok I was just a bit confused because it wouldn’t make sense without the t otherwise it’s just saying r is a multiple of h which doesn’t show how it varies with time.