Volume of a point inside a truncated cone
Hey guys I want to use a 12oz cup to measure things with, but I can't figure out how I would go about doing this. The measurements are roughly 1.1 inch radius at base, 1.6 inch radius on top and 3.8 inch height.
For example, if I wanted to fill it with 4oz of water, how would I calculate what height to fill it at to get this?
Thanks!
You want to use a 12 oz cup to measure things with. The measurements are 1.1 inch at base, 1.6 inch radius and 3.7 inch height.
The formula you're searching for says
Volume = pi/3*h(R^2+R*r+r^2)where R is the larger radius
Since I'm from Europe I gotta love the metric systemOriginally Posted by nucci93
Use the given formula and solve for the unknown variables. I'll walk you through this:
The formula says
Volume = pi/3*h(R^2+R*r+r^2)
We also know that the relationship between the height and the larger radius (top) is
h/R = 3.7/1.6 <=> h = 3.7R/1.6
In this case we then have
Volume = pi/3*h(R^2+R*r+r^2) => 4.5 = pi/3*h(R^2+R*1.1+1.1^2)You can solve this equation by first using the above given relationship between R and h into this equation. This will give you only h as unknown to solve for.
in addition to converting ounces to cubic inches, you would need to use concepts from calculus (volumes of rotation) to solve this problem.
= upper radius of the glass
= lower radius
= glass height
= height to fill for desired volume
= desired volume in cubic inches
convert your desired volume to cubic inches, substitute in the radii and height measurements of the glass ... solve for
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