Question

The inner edge of a circular running-track is
440 m long. If the track is 10 m wide, find the
length of the outer edge of the track.
​

Answer 1

$\mathcal{\green{\underline{\blue{GIVEN:}}}}$

• The inner edge of the circular track (Blue coloured line) = 440m.
• Track is 10 meters wide. (AB = 10m).

$\mathcal{\green{\underline{\blue{TO \:\: FIND:}}}}$

• We need to find the length of the outer track (black coloured line).

$\mathcal{\green{\underline{\blue{SOLUTION:}}}}$

Let us take O as the centre of the circle. The diameter of the bigger circle will be OB and the diameter of the smaller circle is AO. To find OB, we need to find AO and AB.

In the smaller circle:

• Circumference = 440 m.

• $\sf \pi =\frac{22}{7}$

We know that:

$\sf Circumference \: = 2 \times \pi \times r$

$\sf 440 = 2 \times \frac{22}{7} \times AO$

$\sf AO= \frac{440 \times 7 }{22 \times 4}$

$\boxed{\sf{\blue{AO=70m.}}}$

Now, we know that OB=AO+AB.

⇒OB=70+10

⇒OB=80m.

Now, the circumference of the bigger circle:

$\sf Circumference \: \: of \: \: bigger \:\: circle = 2 \times \pi \times R$

$\sf Circumference = 2 \times \frac{22}{7} \times 80$

$\boxed{\sf{\blue{Circumference = 502.85m.}}}$

LENGHT OF THE OUTER TRACK = 502.85m.