24. Selvi's house has an overhead tank in the shake ofa cylinder. This

1.	24. Selvi's house has an overhead tank in the shake ofa cylinder. This is filled by pumping water from asump (an underground tank) which is in the shapeof a cuboid. The sump has dimensions 1.57 m x1.44 m .95 m. The overhead tank has its radius60 cm and height 95 cm. Find the height of thewater left in the sump after the overhead tank hasbeen completely filled with water from the sumpwhich had been full. Compare the capacity of thetank with the of the sump. (Use3.14).
Answer» Dimensions of cylindrical tank are — Radius (r₁) = 60 cm = 0.60 m Height (h₁) = 95 cm = 0.95 m ∴ Volume of Tank = πr²h = 3.14 × 0.6 × 0.6 × 0.95 V1= 1.074 m³ The dimensions of cuboid shape sump are — Length (l) = 1.57 m Breadth (b) = 1.44 m Height (h) = 0.95 m ∴ Volume of the sump =l.b.h. = 1.57 × 1.44 × 0.95 m³ V2= 2.148 m³ When the tank is completely filled from the sump, remained volume of the sump = V2– V1 = 2.148 – 1.074 = 1.074 m³ Now the length and breadth will remain same for the sump but height of water level will decrease due to decrease in water level. ∴ Volume of the water in the sump =l × b×h₂ ⇒ 1.978 = 1.57 × 1.44 ×h₂h₂= 0.475m Hence, the height of water, left in the tank = 0.475 m. and the Volumes of tank and sump are V₁= 1.074 m³&V₂= 2.148 m³respectively v₁/v₂₌1.074/2.148= 1/2

24. Selvi's house has an overhead tank in the shake ofa cylinder. This is filled by pumping water from asump (an underground tank) which is in the shapeof a cuboid. The sump has dimensions 1.57 m x1.44 m .95 m. The overhead tank has its radius60 cm and height 95 cm. Find the height of thewater left in the sump after the overhead tank hasbeen completely filled with water from the sumpwhich had been full. Compare the capacity of thetank with the of the sump. (Use3.14).

Answer»

Dimensions of cylindrical tank are —

Radius (r₁) = 60 cm = 0.60 m

Height (h₁) = 95 cm = 0.95 m

∴ Volume of Tank = πr²h

= 3.14 × 0.6 × 0.6 × 0.95

V1= 1.074 m³

The dimensions of cuboid shape sump are —

Length (l) = 1.57 m

Breadth (b) = 1.44 m

Height (h) = 0.95 m

∴ Volume of the sump =l.b.h.

= 1.57 × 1.44 × 0.95 m³

V2= 2.148 m³

When the tank is completely filled from the sump, remained volume of the sump = V2– V1

= 2.148 – 1.074

= 1.074 m³

Now the length and breadth will remain same for the sump but height of water level will decrease due to decrease in water level.

∴ Volume of the water in the sump =l × b×h₂

⇒ 1.978 = 1.57 × 1.44 ×h₂h₂= 0.475m

Hence, the height of water, left in the tank = 0.475 m.

and the Volumes of tank and sump are

V₁= 1.074 m³&V₂= 2.148 m³respectively

v₁/v₂₌1.074/2.148= 1/2