The volume of a test tube

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Question from Nick, a student:

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)!!

Hi Nick,

Your last sentence says "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)!!"

The bottom of the test tube is not a half-circle it's a half sphere. The volume of a sphere of radius r mm is 4/3 π r³ cubic mm so add half the volume of a sphere of radius 31/2 mm to the volume of the cylindrical portion of the test tube.

Write back if you need more assistance,
penny

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