Avoiding the Overfilled Can

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Upper and Lower bounds
(care of thirdspacelearning.com)

The Problem:

A production line fills 9.0 litres of paint into a cylindrical can of diameter 30cm.

What is the maximum (and minimum) height of the paint in the filled can?



The paint can is cylindrical and the formula for the volume, V, of cylinder is V=πr2h where the radius, r=15cm and V=9.0lt=9000cm3.

Which leads to

h=9000π(15)2 =10πcm =12.73cm(to 2 d.p.)

But this question is really about bounding (upper and lower) because it asks for the maximum height of the paint. To get the maximum height we need to recalculate with the upper bound of the volume, Vupper=9.05lt=9050cm3 and the lower bound of the radius, rlower=29.52=14.75cm.

Using these values we get

hupper=9050π(14.75)2 =13.24081342...cm

Similarly for

hlower=8950π(15.25)2 =12.24992628...cm

So h=12.7±0.5cm.

Further Reading:

Volume of 3-D Shapes
(care of mmerevise.co.uk)

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Is this Quadrilateral a Parallelogram?

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