## 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, `r`^{2} = (`r` 8)^{2} + 50^{2} = `r`^{2} 16`r` + 64 + 2500

16`r` = 2564 `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