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The volume of a test tube 2010-05-20
From Nick:
A maths question. I have a test tube (basically a cylinder but with a rounded bottom end) and the measurements are: the diameter or width of the tube is 31mm and the total length of the whole tube is 204mm. The question is:
(a) what's the volume of this test tube (rounded to the nearest cubic mm) and
(b) what's the capacity of this test tube (rounded to the nearest mL). I need to show the full mathematical workings out of the two, not just the answer. The problem is the circular bottom end of the tube, it isn't flat, that would make it rather "easy"or straightforward but this is a half-circle (like all test tubes are)!!

Answered by Penny Nom.
Measurements on a test tube 2007-10-30
From Bruce:
I figure that the surface area (SA) of a round bottom test tube can be determined by the equation SA = 2pi*h*r where r is the radius of the hemispheric bottom & column part, and h is the height (h) at any point upwards from the bottommost portion in the center of the tube.

I haven't been able to come up with an equation yet for the circumference of such a test tube at any point upwards along the tube based on the height in its center or on the distance along the outside of the tube.

Answered by Harley Weston.



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