The rain water from a roof 22 m × 20 m drains into a cylindrical vessel having a diameter of 2 m and height 3.5 m. If the vessel is just full, then the rainfall (in cm) is:

Solution (By Examveda Team)

Volume of vessel = Volume of roof
π × r² × h = 22 × 20 × x   (where x is rainfall in cm)
$$\eqalign{ & \Rightarrow \frac{{22}}{7} \times \frac{{100 \times 100 \times 350}}{{22 \times 20 \times 100 \times 100}} = {\text{x}} \cr & \Rightarrow {\text{x}} = 2.5{\text{ cm}} \cr} $$