What part of a ditch, 48 m long 16.5 m broad and 4 m deep can be filled
What part of a ditch, 48 m long 16.5 m broad and 4 m deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 m and length 56 m ?
A$$\frac{1}{9}$$
B$$\frac{2}{9}$$
C$$\frac{7}{9}$$
D$$\frac{8}{9}$$
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Answer is : b.) \(\frac{2}{9}\)
Explanation:
Volume of the earth dugout as a tunnel = πr2h
= \(\Big(\frac{22}{7}\Big) \times 2 \times 2 \times 56 \)
= \(\text{704 }m^3 \)
\(\text{Volume of the ditch = }\frac{(48 \times 33)}{(2)}\times 4 \implies 24 \times 33 \times 4 \implies \text{3168 }m^3 \)
∴ \(\text{Part required = }\frac{704}{3168} \implies \frac{2}{9}\)
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