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The length of a semi-circular tunnel is 2 km and diameter is 7 m. Find the expenditure for digging the tunnel at the rate of Rs. 600 per $m 3$ . Find the expenditure for plastering inner side of the tunnel at the rate of Rs. 50 per $m 2$ . $π = 227$

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Detailed Solution

Given, length of the semi-circular tunnel, say

l

is equal to 2km, which is equal to 2000m.
And the diameter of the tunnel is 7m.
We know that the diameter is double the radius.
Then, the radius of the semi-circular tunnel, say

r

72 m

Now, the volume of the semi-circle is half the volume of the circular tunnel.
Therefore, the volume of the circular tunnel is

= 12 × π r 2 l

Substituting the values,

= 12 × 2277272 (2000) ⇒ 11 × 0.5 × 3.5 × 2000 ⇒ 38500 m 2

Then, the expenditure of digging the tunnel at the rate of Rs. 600 per

m 3

= 38500 × 600 = R s . 2, 31, 00, 000

So, option 4 is correct.

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