Question

Rain water which falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius
20 cm. What will be the height of water in the cylindrical vessel if the rainfall is 1 cm. Give your answer to the nearest whole number.
(Use π = 3.14)

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{surface},l=6\mathrm{m}=600\mathrm{cm}, \\ \mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{surface},b=4\mathrm{m}=400\mathrm{cm}, \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{rainfall},h=1\mathrm{cm}\mathrm{and} \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel},R=20\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{water}\mathrm{in}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel}\mathrm{be}H. \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{water}\mathrm{in}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel}=\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{rainfall}\mathrm{in}\mathrm{the}\mathrm{rectangular}\mathrm{surface} \\ \Rightarrow \mathrm{\pi }{R}^{2}H=lbh \\ \Rightarrow 3.14\times {20}^2\times H=600\times 400\times 1 \\ \Rightarrow 1256H=240000 \\ \Rightarrow H=\frac{240000}{1256} \\ \Rightarrow H=191.08\mathrm{cm} \\ \therefore H\approx 191\mathrm{cm} \end{gathered}$$

So, the height of water in the cylindrical vessel is 191 cm.