Question

the radii of the inner and outer circumference of a circular running track are 63m and 70m respectively. find: the area of the track and the difference between the length of the two circumference of the track

Answer 1

Area of track =
$\pi( {70}^{2} - {63}^{2} ) \\ \pi(4900 - 3969) \\ \pi \times 931 \\ \frac{22}{7} \times 931 \\ 2926$
Area of Track is 2926 sq. meter

Circumference of Inner circle =
$2 \times \pi \times r \\ 2 \times \frac{22}{7} \times 63 \\ 396$
Circumference of inner circle = 396 mtrs.

Circumference of outer circle =
$2 \times \frac{22}{7} \times 70 \\ 440$
Circumference of outer circle = 440 mtrs.

Difference = 440 - 396
= 44 mtrs

Answer 2

$radius \: of \: outer \: circumference = r_{1} = 70 \: cm \\ radius \: of \: inner \: circumference \: = r_{2} = 63 \: cm \\ \\ {1}^{st} \: part \: \\ \\ area \: of \: track \: = \pi { r_{1} }^{2} - \pi { r_{2} }^{2} \\ = > \pi( { r_{1} }^{2} - { r_{2} }^{2} ) \\ = > \frac{22}{7} ( {70}^{2} - {63}^{2} ) \\ = > \frac{22}{7} (4900 - 3969) \\ = > \frac{22}{7} \times 931 \\ = > 2926 \: {m}^{2} \\ \\ {2}^{nd} \: part \\ \\ outer \: circumference = 2\pi r_{1} \\ = > 2 \times \frac{22}{7} \times 70 \\ = > 440 \: cm \\ inner \: circumference \: = 2\pi r_{2} \\ = > 2 \times \frac{22}{7} \times 63 \\ = > 396 \\ difference \: = 440 - 396 \\ = > 44 \: cm$