The rainwater from a roof of dimensions 22 , | vedclass

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(C) Given,length of roof $= 22 \, m$ and breadth of roof $= 20 \, m$.Let the rainfall be $a \, cm = \frac{a}{100} \, m$.Volume of water collected on t

Vedclass · Accepted Answer

$2.5$

Vedclass · Answer

(C) Given,length of roof $= 22 \, m$ and breadth of roof $= 20 \, m$.Let the rainfall be $a \, cm = \frac{a}{100} \, m$.Volume of water collected on the roof $= 	ext{length} 	imes 	ext{breadth} 	imes 	ext{height of rainfall} = 22 	imes 20 	imes \frac{a}{100} = \frac{22a}{5} \, m^3$.Radius of the cylindrical vessel $r = \frac{	ext{diameter}}{2} = \frac{2}{2} = 1 \, m$.Height of the cylindrical vessel $h = 3.5 \, m = \frac{7}{2} \, m$.Volume of the cylindrical vessel $= \pi r^2 h = \frac{22}{7} 	imes (1)^2 	imes \frac{7}{2} = 11 \, m^3$.Since the water collected from the roof fills the vessel,the volumes are equal:$\frac{22a}{5} = 11$.$a = \frac{11 	imes 5}{22} = 2.5 \, cm$.Thus,the rainfall is $2.5 \, cm$.

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

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