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

(i) Given:

Radius of outer circle = 70 m

Radius of inner circle = 63 m

Area of circular track = Area of outer circle - Area of inner circle

As we know, the area of the circle = πr²

Area of circular ring =

$\dfrac{22}{7} \times 70^2 - \dfrac{22}{7} \times 63^2\\[1em] = \dfrac{22}{7} \times 4,900 - \dfrac{22}{7} \times 3,969\\[1em] = \dfrac{1,07,800}{7} - \dfrac{87,318}{7}\\[1em] = \dfrac{1,07,800 - 87,318}{7}\\[1em] = \dfrac{20,482}{7}\\[1em] = 2,926 \text{ m}^2$

Hence, the area of the circular track is 2,926 m².

(ii) The difference between the lengths of the two circumferences of the track = Circumference of outer circle - Circumference of inner circle

As we know, the circumference of the circle = 2πr

The difference between the lengths of the two circumferences of the track =

$2 \times \dfrac{22}{7} \times 70 - 2 \times \dfrac{22}{7} \times 63\\[1em] = \dfrac{44}{7} \times 70 - \dfrac{44}{7} \times 63\\[1em] = \dfrac{3080}{7} - \dfrac{2772}{7}\\[1em] = \dfrac{3080 - 2772}{7}\\[1em] = \dfrac{308}{7}\\[1em] = 44 \text{ m}$

Hence, the difference between the lengths of the two circumferences of the track is 44 m.