Question

A subway track must pass through a cylindrical tunnel. The tunnel is 6m in diameter. How wide should the track bed be so that the maximum height at the centre of the tracks is 4.5m? Express your answer to the nearest tenth of a metre.

The answer is 5.2m but I don't understand how you get to that.

Answer 1

See below.

Explanation:

From diagram:

Let the diameter be the chord `AB`

Let the track width be the chord `CD`

`AB` divides `CD` at the midpoint.

We need to find the length of `CD`

Using the intersecting chords theorem which states:

`4.5xx1.5=x xx x`

`6.75 =x^2`

`x=sqrt(6.75)`

`CD=2x=>2sqrt(6.75)=5.196152423`

`5.2m` to nearest tenth of a metre.