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Question
The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.
Calculate:
- its volume,
- the surface area of the tunnel (excluding the floor) and
- its floor area.
Solution
Side of square = 7 m
Radius of semicircle = `7/2` m
Length of the tunnel = 80 m
Area of cross-section of the front part = `a^2 + 1/2pir^2`
= `7 xx 7 + 1/2 xx 22/7 xx 7/2 xx 7/2`
= `49 + 77/4 m^2`
= `(196 + 77)/4`
= `273/4 m^2`
i. Therefore, volume of tunnel = area × length
= `273/4 xx 80`
= 5460 m3
ii. Circumference of the front of tunnel
= `2 xx 7 + 1/2 xx 2pir`
= `14 + 22/7 xx 7/2`
= 14 + 11
= 25 m
Therefore, surface area of the inner part of the tunnel
= 25 × 80
= 2000 m2
iii. Area of floor = l × b
= 7 × 80
= 560 m2
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