What part of a ditch, 48 metres long, 16.5 metres board 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: Option B

Solution(By Examveda Team)

Volume of earth dug :
$$\eqalign{ & = \left( {\frac{{22}}{7} \times 2 \times 2 \times 56} \right){{\text{m}}^3} \cr & = 704\,{{\text{m}}^3} \cr} $$
Volume of ditch :
$$\eqalign{ & = \left( {48 \times 16.5 \times 4} \right){{\text{m}}^3} \cr & = 3168\,{{\text{m}}^3} \cr} $$
∴ Required fraction :
$$\eqalign{ & = \frac{{704}}{{3168}} \cr & = \frac{2}{9} \cr} $$