Question

A school ground is in the shape of a circle with radius 103 m. Four tracks each of 3 m wide has to be constructed inside the ground for the purpose of track events. Find the cost of constructing the track at the rate of ₹ 50 per sq.m

Answer 1

Radius of the ground R = 103 m

Width of a track W = 3 m

Width of 4 tracks = 4 × 3 = 12 m

Radius of the ground without track

r = (103 – 12) m

r = 91 m

Area of 4 tracks = Area of the ground – Area of the ground without track

= πR² – πr² sq.units

= π(R² – r²) sq.units

= `22/7 [103^2 - 91^2]`

= `22/7 [103 + 91] [103- 91]  "m"^2`

= `22/7 xx 194 xx 12`

= `51216/7`

= 7316.57 m² 

∴ Area of 4 tracks = 7316.57 m²

Cost of constructing 7316.57 m² = ₹ 50

∴ Cost of constructing 7316.57 m² = ₹ 50 × 7316.57

= ₹ 3,65,828,57

Cost of constructing the track ₹ 3,65,828,57