Question

The rain water from a roof of dimensions $22\mathrm{m}\times 20\mathrm{m}$ 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 .

Answer 1

The dimension of the roof is $22\mathrm{m}\times 20\mathrm{m}$.
Diameter of the cylinderical vessel = 2 m
Radius of the cylinderical vessel, R = 1 m
Height of the cylinderical vessel, H = 3.5 m
Let the height of the roof be h.
Volume of water thus collected on the roof = $22\times 20\times h$
Volume of the cylinderical vessel = $\mathrm{\pi }{\left(\mathrm{R}\right)}^2\mathrm{H}=\mathrm{\pi }{\left(\frac{2}{2}\right)}^2\times 3.5=\mathrm{\pi }\times 1\times 3.5=3.5\mathrm{\pi }$
Volume of water collected on the roof = Volume of the cylinderical vessel
$$\begin{gathered} 22\times 20\times h=3.5\mathrm{\pi } \\ \Rightarrow \mathrm{h}=\frac{3.5\mathrm{\pi }}{22\times 20}=0.025\mathrm{m} \\ \Rightarrow \mathrm{h}=2.5\mathrm{cm} \end{gathered}$$