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What part of a ditch 48m long 16.5 broad and 4m deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4m and length 56m?

Correct answer: B. 2/9

  • A. 1/9
  • B. 2/9
  • C. 7/9
  • D. 8/9

Explanation

The cylindrical tunnel gives volume πr2h = (22/7) × (2 m)2 × 56 m = 704 m3. The ditch volume is 48 m × 16.5 m × 4 m = 3168 m3, so the fraction filled is 704 m3 ÷ 3168 m3 = 2/9. The likely wrong choice is 1/9, which comes from losing a factor of 2 in the circular area or ditch calculation.

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