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?

### Concept & Volume Equivalence When water is transferred from one container to another, its volume remains constant. We equate the volume of water on the rectangular surface to the volume of water in the cylindrical vessel. $$ V_{\text{cuboid}} = V_{\text{cylinder}} $$ $$ l \times b \times h_1 = \pi \times r^2 \times h_2 $$ ### Step-by-Step Solution - **Given:** - Length of surface $l = 6$ m $= 600$ cm - Breadth of surface $b = 4$ m $= 400$ cm - Rainfall height $h_1 = 1$ cm - Radius of cylinder $r = 20$ cm - **Calculation:** - Volume of rainfall $= l \times b \times h_1 = 600 \times 400 \times 1 = 240000$ cm$^3$. - Volume of water in cylinder $= \pi \times r^2 \times h_2 = \frac{22}{7} \times (20)^2 \times h_2 = \frac{8800}{7} \times h_2$. - Equating both volumes: - $240000 = \frac{8800}{7} \times h_2$ - $h_2 = \frac{240000 \times 7}{8800} = \frac{2400 \times 7}{88} = \frac{300 \times 7}{11} = \frac{2100}{11} \approx 190.9$ cm. - The closest value among the options is $191$ cm. ### Exam Strategy & Shortcut Always convert all dimensions to the same unit (cm) before calculating. ### Common Pitfall Forgetting to convert meters to centimeters for the rectangular surface length and breadth. ### Final Answer Therefore, the correct answer is **191 cm**.