help on equations of a wine glassi have an assignment to do the wine glass for maths and i dont know any equation.  it has a table with colums that say ; glass part (eg. base, stem and body),...

help on equations of a wine glass

i have an assignment to do the wine glass for maths and i dont know any equation.  it has a table with colums that say ; glass part (eg. base, stem and body), function, domain and coordinates in mm.

it should have at least 6 functions please help and i dont want a glass that is too complecated.

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted on

The simplest wine glass structure to use would have a cylindrical base, a cylindrical stem, and a half-sphere body. 

Give the following dimensions of the wine glass:

radius of base, height of base, radius of stem, height of stem, and radius of body

Provide the following equations for surface area:

SA of cylindrical base = 2 * pi * r^2 + 2 * pi * r * h

SA of cylindrical stem = 2 * pi * r^2 + 2 * pi * r * h

SA of half-sphere body = (4 * pi * r^2) / 2

To find the total surface area of the wine glass, add the three answers above.

Next, provide the following equations for volume:

V of cylindrical base = pi * r^2 * h

V of cylindrical stem = pi * r^2 * h

V of half-sphere body = (4/3 * pi * r^3) / 2

To find the total volume of the wine glass, add the three answers above.

So here is how I would phrase the question.

A wine glass has a cylindrical base, a cylindrical stem, and a half-sphere body.  The base has a height of __ mm and a radius of __ mm.  The stem has a height of __ mm and a radius of __.  The body has a radius of __ mm.  Use this information to find the total surface area and the total volume of the wine glass.

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