Rain from a roof \(22\,\text{m}\times20\,\text{m}\) drains into a cylindrical vessel of diameter 2 m and height 3.5 m. If the vessel is just filled, find the rainfall in cm.
2.5 cm
Step 1: Write the given data.
Step 2: Find the volume of water collected in the cylindrical vessel (this equals the volume of rainwater fallen on the roof).
Volume of cylinder = \(\pi r^2 h\)
\(= \dfrac{22}{7} \times (1)^2 \times 3.5\)
\(= 11\,\text{m}^3\)
Step 3: Let the depth of rainfall be \(x\,\text{m}\). Then, volume of rainwater on the roof = roof area × rainfall depth.
Roof area = \(22 \times 20 = 440\,\text{m}^2\)
So, volume of rainwater = \(440 \times x\,\text{m}^3\)
Step 4: Since all the rainwater fills the vessel, equate the two volumes:
\(440x = 11\)
\(x = \dfrac{11}{440} = 0.025\,\text{m}\)
Step 5: Convert to cm:
\(0.025\,\text{m} = 0.025 \times 100 = 2.5\,\text{cm}\)
Final Answer: Rainfall = 2.5 cm