Problem from RS Aggarwal book, problem number 22, page number 811, exercise 17B, chapter volume and surface area of solid.

Chapter Mensuration

Deepak BoraNewbie

# The rain water from a 22 m × 20 m roof drains into a cylindrical vessel of diameter 2 m and height 3.5 m. If the rain water collected from the roof fills 4/5th of the cylindrical vessel, then find the rainfall in centimeter.

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Given data,

Roof length = 22 meter, roof width = 20 meter,

Roof height = ?

Cylindrical Vessel diameter = 2 meter,

Vessel radius =1 meter,

vessel height = 3.5 meter

Roof height (h) = rainfall height

Volume of water on roof = volume of water in cylinder

1 meter = 100 cm

Volume of cylinder = [πr²h] * [4/5] ……..fills 4/5th of the cylindrical vessel

Volume of roof = l*b*h

l*b*h= πr²h * [4/5]

22*20*h = ((22/7)*1*3.5) * [4/5]

22*20*h = 11 * [4/5]

h = [4/5]/40 meter

h = ( * [4/5] /40)*100 cm

h= rainfall = 2 cm

∴ rainfall = 2 cm