3.
The length of a semicircular tunnel is 2 km and diameter is 7 m. Find the
expenditure for digging the tunnel at the rate of 600 per m². T = =
Answers
The length of a semicircular tunnel is
2
2
km
km
and diameter is
7
7
m
m
. Find the expenditure for digging the tunnel at the rate of Rs.
600
600
per
m^{3}
m
3
. Find the expenditure for plastering inner side of the tunnel at the rate of Rs.
50
50
per
m^2
m
2
.
\left (\pi = \dfrac {22}{7}\right )
(π=
7
22
)
Asked on December 27, 2019 byavatar
Annie Kankate
ANSWER
Length of the semicircular tunnel
= 2
=2
km
km
.
\therefore l = 2000
∴l=2000
m
m
Diameter of the semicircular tunnel
= 7
=7
m
m
\therefore
∴
Radius of tunnel
= \dfrac {7}{2}
=
2
7
\therefore r = 3.5
∴r=3.5
m
m
Volume of semicircular tunnel
= \dfrac {1}{2}\times
=
2
1
×
Volume of circular tunnel
= \dfrac {1}{2}\times \pi r^{2} l
=
2
1
×πr
2
l
= \dfrac {1}{2} \times \dfrac {22}{7}\times 3.5\times 3.5\times 2000
=
2
1
×
7
22
×3.5×3.5×2000
= 11\times 0.5\times 3.5\times 2000
=11×0.5×3.5×2000
= 11\times 5\times 35\times 20
=11×5×35×20
= 38500\ m^{3}
=38500 m
3
\therefore
∴
Expenditure for digging (semicircular) the tunnel at the rate Rs.
600
600
per
m^{3}
m
3
= 38,500\times 600
=38,500×600
=
=
Rs.
2,31,00,000
2,31,00,000
\therefore
∴
Expenditure for plastering inner side of the tunnel at the rate of Rs.
50
50
per
m^2
m
2
= 22000\times 5
=22000×5
=
=
Rs.
11,00,000
11,00,000