Question

The radii of the inner and outer circumferences of a circular running track are 63 m and 70 m respectively. Find :
(i) the area of the track ;
(ii) the difference between the lengths of the two circumferences of the track.

Answer 1

Outer radius, r₁ = 70 m

Inner radius, r₂ = 63 m

∴ Area of track = `pir_1^2 - pir_2^2`

= `22/7[(70)^2 - (63)^2]`

= `22/7(70 + 63)(70 - 63)`

= `22/7 xx 133 xx 7`

= 2926 m²

Length of outer edge i.e. circumference

= `2pir_1`

= `2 xx 22/7 xx 70 = 440`m

Length of inner edge = `2pir_2`

= `2 xx 22/7 xx 63 = 396` m

Difference between lengths of two circumferences = 440 – 396 = 44 m
Hence (i) 2926 m² (ii) 44 m