What part of a ditch, 48 metres long, 16.5 metres board and 4 metres deep can be

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Question

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 ?

Options:

A . $$\frac{1}{9}$$

B . $$\frac{2}{9}$$

C . $$\frac{7}{9}$$

D . $$\frac{8}{9}$$

Answer: Option B
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 :
$$\eqalign{
& = \frac{{704}}{{3168}} \cr
& = \frac{2}{9} \cr} $$

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