Question 621373
Since you placed that question under "Quadratic Equation", I assume the expected profile is a parabola, the graph of a quadratic function. I inspected all the wine glasses in my china cabinet and in my wine cupboard and concluded that a paraboloid is not the shape of a wine glass. The mouth of the glass is never the widest part. Wine glasses can be shaped like truncated ellipsoids (white wine glasses) or have a truncated egg shape (with the tip cut off). The bulb of wine glasses is not shaped like a paraboloid, but I guess a paraboloid is the simple shape envisioned. (I would suggest a truncated ellipsoid, but you may not have studied ellipses yet).
I also assume that you are in a Calculus class and were taught how to use integration to find the volume of a solid of revolution.
If the height above the bottom of the bulb is {{{h}}} and the cross-section radius is {{{x}}}, the shape of a paraboloid wine glass bulb would given by
{{{h=ax^2}}} <--> {{{x^2=h/a}}}
A cross section of the glass is a circle with area {{{pi*x^2}}},
and since {{{x^2=h/a}}}, that cross section area would be {{{pi*h/a}}}
If the height of the bulb (vertical distance from the rim to the bottom of the bulb) is H, the volume could be calculated as
{{{V=int((pi/a)*h,dh,0,H)}}}
If you use centimeters, then you would get the volume in cubic centimeters, which are essentially the same as milliliters.
I would chose something close to 6-8 cm for the diameter at the top, and 10 cm for the height (H) of the wine glass bulb.
With a paraboloid shape, and an 8-cm top diameter, you have x=4 and h=10 at the rim, so
{{{10=a*4^2}}} --> {{{a=10/16=5/8}}}.
In that case
{{{V=int((5pi/8)*h,dh,0,10)=(5pi/8)*10^2}}}= about 196 mL