Question

The radii of the inner and outer circumferences of a circular -rinning -track are 63 m and 70 m respectively. Find:

(i) The area of the track

(ii) The difference between the lengths of the two circumference of the track

Answer 1

Outer radius, $r_1=70m$

Inner radius, $r_2=63m$

$\therefore$ Area of track $=\pi r_1^2-\pi r_2^2$

$=\frac{22}{7}\left[\right(70{)}^2-\left(63{)}^2\right]$

$=\frac{22}{7}(70+63)(70-63)$

$=\frac{22}{7}\times 133\times 7$

$=2996m^2$

Length of outer edge i.e. circumference

$=2\pi r_1$

$=2\times \frac{22}{7}\times 70=440m$

Length of inner edge $=2\pi r_2$

$=2\times \frac{22}{7}\times 63$

=396 m

$\therefore$ Difference between lengths of two circumferences

=440-396

=44 m

Hence (i)2926 $m^2$ (ii)44 m