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 a rainfall of 1 cm has fallen ?

Answer 1

Length of rectangular surface (L) = 6 m = 600 cm
Breadth of rectangular surface (B) = 4 m = 400 cm
Height of rectangular surface (H) = 1 cm
Radius of cylindrical vessel (r) = 20 cm
Let the height of cylindrical vessel = h cm
Volume of rectangular surface = Volume of cylindrical vessel
⇒ L $\times$ B $\times$ H = $\pi r^{2}h$
⇒ 600 $\times$ 400 $\times$ 1 = $\pi \times {20}^2\times h$
⇒ h = 190.90 cm
∴ Height of the cylindrical vessel is 190.90 cm.