Ramesh has build recently his house and installed an underground tank and
overhead tank. Dimensions of tanks are as follows :
Underground Tank: Base 2m X 2m and Height 1.1 m.
Overhead tank: Radius 50 cm and Height 175 cm.
On the basis of the above information, answer the following questions:
(i) What is the capacity of thesump?
(a) 2200 litres b) 44000 litres
(c) 4400 litres d) 22000 litres
(ii) What is the ratio of the capacity of the sump to the capacity of the
overhead tank?
(a) 1.75 b) 1.25
(c) 2.5 d) 3.2
(iii) If curved part of overhead tank need to be painted to save it from
corrosion, how much area need to be painted?
(a) 5.5 m2 b) 3.3m2
(c) 2.5 m2 d) 4.5m2
(iv) If water is filled in the overhead tank at the rate of 11 litre per minute,
the tank will be completely filled in how many time?
(a) 65minutes b) 62.5 minutes
(c) 130 minutes d) 125 minutes
(v) If the amount of water in the sump, at an instant, is 2400 litres, then the
water level in the sump at that instant is
(a) 60 cm b) 69.3 cm
(c) 70 cm d) 60.9 cm
20 In the sport of cricket the captain sets the field according to a plan.
Answers
Step-by-step explanation:
Clearly the volume of the water in the overhead tank is equal to the volume of the water removed from the sump.
Now Volume of water in the overhead tank =3.14×0.6×0.6×0.95m
3
=3.14×0.36×0.95m
3
Volume of water in the sump when it is full of water =1.57×1.44×0.95m
3
=1.57×4×0.36×0.95m
3
=2×3.14×0.36×0.95m
3
Volume of water left in the sump after filling the tank
(2×3.14×0.36×0.95−3.15×0.36×0.95)m
3
=3.14×0.36×0.95m
3
Area of the base of the sump =1.57×1.44m
3
=1.57×4×0.36m
3
=2×3.14×0.36m
3
Height of the water in the sump =
2×3.14×0.36
3.14×0.36×0.95
m=
2
0.95
=47.5cm
Now
capacityofsump
capacityoftank
=
2×3.14×0.36×0.95
3.14×0.36×0.95
=
2
1
Answer:
↓
Step-by-step explanation:
(i) Volume of underground tank,
lbh = = 2 2 # # 1 1. . 4 4 m3
Since 1 m3 is equal to 1000 litres,
4.4 m3 = = 4 4. # 1000 4400 litres
Thus (c) is correct option.
(ii) Radius of overhead is 50 cm i.e. 2
1 meter and
height is 175 cm i.e. 1 7. 5 4 = 7 metre.
Thus volume of overhead tank,
r hcy
2 π 7
22
2
1
2
1
4
7
8
11 m3 = = ###
Capacity of tank
Capacity of sump
Overhead r h
lbh
cy 2 π =
4 4.
8
= 11 = 3 2.
Thus (d) is correct option.
(iii) C.S.A. of cylindrical tank
2π rhcy 2 . 7
22
2
1
4
7 5 5 m2 = = # # #
Thus (a) is correct option.
(iv) Volume of water in cylindrical tank is 8
11 m3 .
8
11 m3
8
11 = # 1000 litres
Thus time taken to fill tank,
8
11 1000 11
1 = = # # 125 minutes
Thus (d) is correct option.
(v) Volume of water in underground tank
= 2400 litres 2.4 m3 =
Then, V = lbh1
2 2 # # h1 = 2 4.
h1 . 2 2
2 4
# = = 0 6. m = 60 cm
Thus (a) is correct option.