1.

Rainwater, which falls on a flat rectangular rooftop of dimensions 22m by 10m, is transferred into a cylindrical vessel of internal radius 50 cm through a circular pipe. A certain day recorded a rainfall of 2.5 cm. Find the (i) volume and (ii) height of the water, filled in the cylindrical vessel.

Answer» (i) Volume of water filled in the cylindrical vessel
= volume of water collected on the rooftop
`= (22 xx 10 xx (2.5)/(100)) m^(3) = (11)/(2) m^(3) = 5.5 m^(3)`
(ii) Let the reqiured height of water in the vessel be h metres
Radius of the vessel, `r = (50)/(100)m = (1)/(2) m`
Volume of water in the cylindrical vessel
`= (pi r^(2)h) m^(3)`
`= ((22)/(7) xx (1)/(2) xx (1)/(2) xx h) m^(3) = (11h)/(14) m^(3)`
`:. (11h)/(14) = (11)/(2) rArr = ((11)/(2) xx (14)/(11)) m = 7m`
Hence, the height of water in the cylindrical vessel is 7 m


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