Question

The inner circumference of a circular track is 1408 m and the track is 7 m wide. The cost of levelling the track at Rs. 6 per m² is: (Take π = 22/7)
1. Rs. 59,880
2. Rs. 60,000
3. Rs. 60,060
4. Rs. 57,600

Answer 1

Correct Answer - Option 3 : Rs. 60,060

Given:

Inner circumference of a circular track is 1408 meters 

Track is 7 m wide

Cost of levelling a track at Rs. 6 per m²

Formula Used:

Circumference = 2πr

Area = πr² 

Where,

r is radius

Calculation:

Inner circumference = 2πr

⇒ 1408 = 2 × 22/7 × r

⇒ r = (1408 × 7)/(2 × 22)

⇒ r = 224 meters

Inner radius of circular track (r) = 224 meters

Track is 7 meters wide

Outer radius of circular track (R),

⇒ 7 + 224

⇒ 231 meters

Area of a track = πR² – πr²  

⇒ Area of a track = π(R² – r2) 

⇒ Area of a track = π (R + r)(R – r)

⇒ Area of a track = 22/7 × (231 + 224)(231 – 224)

⇒ Area of a track = 22/7 × 455 × 7

⇒ Area of a track = 22 × 455

Cost of leveling the track,

⇒ Rate × Area of a track

⇒ 6 × 22 × 455

⇒ 60,060

∴ Cost of leveling the track is Rs. 60,060.