C4 differentiation

I don't really understand that highlighted bit in the solution? Is it saying that change in volume in relation to height equals the area at a given point or that it equals the total area of the container? I don't really understand why the highlighted relationship would be true either? ImageUploadedByStudent Room1452370858.488313.jpg

ImageUploadedByStudent Room1452370858.488313.jpg

it's the bit starting at 'but...' not the line above.
Thanks

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Reply 1

EricPiphany

17

The volume is equal to the cross sectional area times the height of the water level, simply because it forms a right prism.
It then differentiates with respect to h.
The rate of change of the volume with respect to the height is equal to the constant cross sectional area.
If you were to plot the volume against the height, it would be a straight line with gradient A.

(edited 8 years ago)

Reply 2

maths_4_life

OP

2

Original post by EricPiphany

The volume is equal to the cross sectional area times the height of the water level, simply because it forms a right prism.
It then differentiates with respect to h.
The rate of change of the volume with respect to the height is equal to the constant cross sectional area.
If you were to plot the volume against the height, it would be a straight line with gradient A.

Is it always true that the rate of change of the volume with respect to the height is equal to the constant cross sectional area, or is it only true in this question? Like is it a general relationship or just something they are giving you to make the question possible?

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Reply 3

maths_4_life

OP

2

Original post by EricPiphany

The volume is equal to the cross sectional area times the height of the water level, simply because it forms a right prism.
It then differentiates with respect to h.
The rate of change of the volume with respect to the height is equal to the constant cross sectional area.
If you were to plot the volume against the height, it would be a straight line with gradient A.

Oh my god I've been so stupid! Last time a try to do maths after drinking! Sorry I get it totally now!

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Reply 4

EricPiphany

17

Original post by maths_4_life

Is it always true that the rate of change of the volume with respect to the height is equal to the constant cross sectional area, or is it only true in this question? Like is it a general relationship or just something they are giving you to make the question possible?

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