What part of a ditch, 48 metres long, 16.5 metres broad and 4 metres deep can be filled by the earth got by… · ABC26GN4927

Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: S.S.C. 2007

What part of a ditch, 48 metres long, 16.5 metres broad and 4 metres deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 metres and length 56 metres?
(a)$\frac{1}{9}$
(b)$\frac{2}{9}$
(c)$\frac{7}{9}$
(d)$\frac{8}{9}$
Answer
Answer (as printed): B
Explanation
Volume of earth dug $=\left(\frac{22}{7} \times 2 \times 2 \times 56\right) \mathrm{m}^{3}=704 \mathrm{m}^{3}$. Volume of ditch $=(48 \times 16.5 \times 4) \mathrm{m}^{3}=3168 \mathrm{m}^{3}$. ∴ Required fraction $=\frac{704}{3168}=\frac{2}{9}$.

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