Question

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☆Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The overhead tank has its radius 60 cm and height 95 cm. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump. (Use π = 3.14)​

Answer 1

Length (/) = 1.57 m

Breadth (b) = 1.44 m

Height (h) = 95 cm = 95 x m = 0.95 m 100

Volume of sump = Length x Breadth x Height

= /bh

= 1.57 X1.44 x95

= 2.147 m³Volume of overhead tank

Height of overhead tank = h = 95 cm = 95x₁0 m = 0.95 m

And, radius = r = 60 cm= 60x - m = 0.6 m

100Volume of overhead tank = r²h

= πx (0.6)² x (0.95)

= 0.342 m³

= 0.342x 3.14

= 1.074 m³

Volume of water left in the cuboidal sump after filling the tank

= Volume of cuboidal sump-Volume of cylindrical tank

= 2.147 1.073

= 1.073 m³

Now,

Volume of water left in cuboidal sump = 1.073

Length x Breadth x Height = 1.73

1.57 x1.44 xh = 1.073

h = 1.073 1.57 x 1.44

h = 0.475 m

h = 0.475 x 100 cm

h = 47.5 cm

So, height of water left in sump = 47.5 cm