The water from a roof, 9 sq. metres in area, flows down to a cylindrical container of 900 cm base. To what height will the water rise in cylinder if there is a rainfall of 0.1 mm?
- 0.1 cm
- 0.1 metre
- 0.11 cm
- 1 cm
The Correct Option is D
Solution and Explanation
To find the height to which water will rise in the cylindrical container, we need to first calculate the volume of water collected from the roof and then determine how high this volume will rise in the cylinder.
1. Calculate the volume of water collected from the roof:
| Area of the roof | = 9 sq. metres |
| Rainfall | = 0.1 mm = 0.01 cm |
| Volume of water (in cubic cm) | = Area × Rainfall = 9 m² × 0.01 cm = 90000 cm² × 0.01 cm = 900 cm³ |
2. Calculate the height the water will rise in the container:
| Volume of cylinder (V) | = πr²h |
| Given volume | = 900 cm³ |
| Base radius (r) | = 900 cm = πr² r = 15 cm |
3. Substitute in the formula for cylinder volume: 900 = π × 15² × h
4. Solve for h: h = 900/(π × 225) h = 1 cm
The water will rise to a height of 1 cm in the cylindrical container.
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