NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes - Exercise 12.4

Question 19

Step 1: Write the given data.

• Roof length = \(22\,\text{m}\)
• Roof breadth = \(20\,\text{m}\)
• Vessel diameter = \(2\,\text{m}\) ⇒ radius = \(1\,\text{m}\)
• Vessel height = \(3.5\,\text{m}\)

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