Consider a cuboidal underground tunnel of length 500 m whose cross-section is given in the figure. If 1 m3 of concrete costs 1000 rupees, find the amount of money needed to build the tunnel.
Explanation:
Total volume of Tunnel = 8 × 16 × 500 = 64000 m3
Radius of the given semicircle = 8 m
Volume of the semi-circle = (π × 8 × 8)/2 × 500 = 32π × 500 = 16000π m3
∴ Volume of the required cross-section = 64000 - 16000π = 16000(4 − π) m3
Total amount of money needed = 16000(4 − π) × 103 = 16(4 − π) × 106 rupees
Hence, option (c).
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