# The Plastic Brain

Here’s my answer for the puzzle I posed earlier:

[1] Use the ruler to measure the height of the cylinder

[2] Trace the bottom of the cylinder to construct a circle

[3] Use the pair of compasses to construct intersecting diameters

[4] Measure the radius of the circle

[5] Mark the cylinder on the top, and roll it along a line from the mark until the mark touches again to measure the circumference.

Now, find the volume by multiplying the area of the circle (A), by the height of the cylinder (h).

Normally you would use π in the formula A=πr² -but that is not allowed.

But did you know that the area of a circle is also given by A=½cr (where c is the circumference)?

As proof, π=c÷2r (by definition), which can be written ½c÷r. Replace π in A=πr² to produce A=½c÷r x r² =½cr.

The volume is therefore given by V=½crh

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An alternative answer was provided by God Damn Batman

Any other answers out there?

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### Author: Rogan Tinsley

Biology, science and maths teacher with a PhD in Neuroscience and passion for education.