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The outer circumference of a circular race-track is 528 metre. The track is everywhere 14 metre wide. Cost of levelling the track at the rate of Rs. 10 per sq. metre is :
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- Rs. 77660
- Rs. 66760
- Rs. 76760
- Rs. 67760
- Rs. 77660
Correct Option: D
External radius of circular path = R metre
∴ 2πR = 528
| ⇒ 2 × | × R = 528 | |
| 7 |
| ⇒ R = | = 84 metre | |
| 2 × 22 |
∴ In-radius (r) = 84 – 14 = 70 metre
∴ Area of path = π(R² – r²)
| = | (84² - 70²) | |
| 7 |
| = | (84 + 70)(84 - 70) | |
| 7 |
| = | × 154 × 14 = 6776 sq. metre | |
| 7 |
∴ Required cost = 6776 × 10 = Rs. 67760
