A ditch measures 48 m in length, 16.5 m in breadth, and 4 m in depth. Earth is obtained by digging a cylindrical tunnel of diameter 4 m and length 56 m. What fraction of the ditch can be filled by this earth?

Introduction / Context:This is a volume-conservation problem: the volume of earth dug from a cylindrical tunnel is used to fill a rectangular ditch. The answer is the ratio of the tunnel volume to the ditch volume.

Given Data / Assumptions:

• Ditch: 48 m × 16.5 m × 4 m.
• Tunnel: cylinder with diameter 4 m ⇒ radius 2 m, length 56 m.
• No loss of earth during transfer.

Concept / Approach:

• Ditch volume V_ditch = L*B*H.
• Tunnel volume V_tunnel = π*r^2*L.
• Fraction filled = V_tunnel / V_ditch.

Step-by-Step Solution:

Verification / Alternative check:Compute exact with π ≈ 22/7: V_tunnel = 224*(22/7) = 704/1 ≈ 704 (close to 703.72). Then 704 / 3168 = 2 / 9. Correct.

Why Other Options Are Wrong:

• 1/9, 7/9, 8/9: Do not match the computed ratio.
• None of these: Incorrect; 2/9 is exact with π = 22/7.

Common Pitfalls:

• Using diameter instead of radius in cylinder volume.
• Arithmetic errors when simplifying the fraction.

Final Answer:2/9