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In a Rain-water Harvesting System, the Rain-water from a Roof of 22 M × 20 M Drains into a Cylindrical Tank Having Diameter of Base 2 M and Height 3·5 M. If the Tank is Full, Find the Rainfall in Cm. - CBSE Class 10 - Mathematics

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In a rain-water harvesting system, the rain-water from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and height 3·5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.

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

Solution

Given:

Length of the roof, l = 22m

Width of the roof, b = 20 m

Base radius of the cylindrical vessel, R = `2/2` = 1 m

Height of the cylindrical vessel, H = 3.5 m

Let the height of the rainfall be h.

Now,

Total amount of rainfall = Volume of rain water collected in the cylindrical vessel.

`lbh = piR^2H`

`=> 22 xx 20 xx h = 22/7 xx (1)^2 xx 3.5`

`=> 440h = 22/7 xx 3.5/440`

`=> h = 0.025 m`

`:. h = 2.5 cm`

Water conservation is very important for sustainable development. Different methods can be used for conservation of water. One such method is rain water harvesting which not only avoids wastage of water but also helps in meeting the water demand during summers

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Solution In a Rain-water Harvesting System, the Rain-water from a Roof of 22 M × 20 M Drains into a Cylindrical Tank Having Diameter of Base 2 M and Height 3·5 M. If the Tank is Full, Find the Rainfall in Cm. Concept: Surface Areas and Volumes Examples and Solutions.
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