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The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.

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The radius of the cylindrical vessel


            Height = 3.5 cm

           \text{ Volume} =\pi r^2 h=\frac{22}{7}\times 1 \times 1 \times \frac{35}{10}=11m^3

            Let the height of rainfall = x

            Length = 22m

            Breadth = 20m

           Volume= l \times b \times h

                        = 22 \times 20 \times x

            Rainfall = volume of water = volume of the cylindrical vessel

                        22 \times 20 \times x=11

                        x=\frac{11}{22 \times 20}=\frac{1}{40}=0.025 m

                        x=0.025 m

            Or        x= 2.5cm        [Q 1 m = 100 cm]

            Hence the rainfall is in 2.5 cm

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