#$&*
PHY 232
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Class notes #7
1)What on earth does 'dy represent? I can see your explanation but I don't understand it and I've been staring at it for about an hour.
Isn't the change in water depth the same as the change in diameter?
2) I can understand that the ratios of Volume and Area are related. But why is the ratio of diameters squared????? ('d2/'d1)^2???
@& I need to know the context to make this clearer, so a copy of the paragraph to which you are referring would be helpful.
However `dy stands for Delta-y, the change in y.
Regarding the squared diameters, the cross-sectional areas of two circles are in the same proportion as the square of their diameters.
Specifically
A_1 = pi r_1^2
A_2 = pi r^2^2
so
A_2 / A_1 = (pi r_2^2) / (pi r_1^2) = (r_2 / r_1_^2
and since diameter = 2 * radius,
d_2 / d_1 = r_2 / r_1
so that
A_2 / A_1 = (d_2 / d_1)^2
as well.
In general the areas of two geometrically similar shapes are in the squared proportion of any of their linear dimensions (e.g., radiii, diameters, diagonals, altitudes, etc..), and the volumes are in the cubed proportion of linear dimensions (e.g., the volumes of two spheres are in the proportion (r_2 / r_1)^3).*@
@& Check my notes and let me know if you have additional questions.*@