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How many cubic metres of earth must be dug out to sink a well of 22.5 m deep and diam 7m ?
- a)866.25 cu m
- b)826.25 cu m
- c)16.25 cu m
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
How many cubic metres of earth must be dug out to sink a well of 22.5 ...
Understanding the Problem
To determine how much earth must be dug out to sink a well, we need to calculate the volume of a cylindrical shape created by the well.
Formula for Volume of a Cylinder
The formula for the volume (V) of a cylinder is:
V = π × r² × h
Where:
- r = radius of the base of the cylinder
- h = height (depth) of the cylinder
- π (Pi) is approximately 3.14
Given Data
- Depth of the well (h) = 22.5 m
- Diameter of the well = 7 m
Calculating the Radius
- Radius (r) = Diameter / 2 = 7 m / 2 = 3.5 m
Calculating the Volume
Now, substituting the values into the volume formula:
- V = π × (3.5 m)² × 22.5 m
Calculating step-by-step:
1. Calculate the radius squared:
- (3.5 m)² = 12.25 m²
2. Multiply by the height:
- 12.25 m² × 22.5 m = 275.625 m³
3. Now, multiply by π (approximately 3.14):
- V ≈ 3.14 × 275.625 m³ = 866.25 m³
Final Conclusion
The total volume of earth that must be dug out to sink the well is approximately 866.25 cubic meters.
Correct Answer
Therefore, the correct answer is option 'A' - 866.25 cu m.
To determine how much earth must be dug out to sink a well, we need to calculate the volume of a cylindrical shape created by the well.
Formula for Volume of a Cylinder
The formula for the volume (V) of a cylinder is:
V = π × r² × h
Where:
- r = radius of the base of the cylinder
- h = height (depth) of the cylinder
- π (Pi) is approximately 3.14
Given Data
- Depth of the well (h) = 22.5 m
- Diameter of the well = 7 m
Calculating the Radius
- Radius (r) = Diameter / 2 = 7 m / 2 = 3.5 m
Calculating the Volume
Now, substituting the values into the volume formula:
- V = π × (3.5 m)² × 22.5 m
Calculating step-by-step:
1. Calculate the radius squared:
- (3.5 m)² = 12.25 m²
2. Multiply by the height:
- 12.25 m² × 22.5 m = 275.625 m³
3. Now, multiply by π (approximately 3.14):
- V ≈ 3.14 × 275.625 m³ = 866.25 m³
Final Conclusion
The total volume of earth that must be dug out to sink the well is approximately 866.25 cubic meters.
Correct Answer
Therefore, the correct answer is option 'A' - 866.25 cu m.
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