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Circular Pipes

Problem

A surveyor places a metre stick against the base of a large circular underground pipe and finds that the midpoint of the stick is 8 cm from the pipe wall.

Use this information to find the inside diameter of the pipe.


Solution

Using the Pythagorean Theorem, r2 = (r minus 8)2 + 502 = r2 minus 16r + 64 + 2500

therefore 16r = 2564 implies r = 160.25

So the internal diameter is 320.5 cm.

What if the stick was 10 cm from the wall?
Can you generalise for any distance x?

Problem ID: 36 (Feb 2001)     Difficulty: 2 Star

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