Q3. Which of the following quantity is measured using a planimeter?
📚 Detailed Explanation: A Planimeter Measures Area
The planimeter is a minor surveying instrument specifically designed to measure the area of any plane figure drawn on paper, regardless of how irregular its boundary is. Unlike geometric formulas that require knowing the shape’s dimensions, a planimeter works directly on the plotted figure by tracing its perimeter.
How a Planimeter Works
The instrument has two arms: a pole arm anchored to a fixed point and a tracer arm guided along the figure’s boundary. As the tracer follows the perimeter in one complete loop, the measuring wheel rolls and skids, recording net displacement. The initial and final wheel readings, substituted into A = M × [F − I ± 10N + C], give the area directly.
Why the Other Options Are Wrong
B (Bar diameter): Bar diameter and other linear dimensions are measured with vernier calipers, micrometers, or steel rules. These are precision length-measuring instruments. A planimeter has no mechanism to measure lengths or diameters.
C (Volume): A planimeter measures 2D area, not 3D volume. However, volumes can be derived by using a planimeter to find cross-sectional areas at regular intervals and then applying the average end-area method or Simpson’s 1/3 rule. The planimeter itself still outputs only area.
D (Weight): Weight is measured with spring balances, weighing scales, or load cells. Planimeters have no connection to force or mass measurement.
Minor Surveying Instruments and What They Measure
| Instrument | Quantity Measured | Typical Use |
|---|---|---|
| Planimeter | Area of irregular plane figures | Cross-sections, catchment areas, land plots on maps |
| Hand Level | Approximate horizontal levels | Preliminary field levelling, slope assessment |
| Abney Level | Vertical angles and slopes | Tracing contours, measuring slope along chain lines |
| Pantagraph | (Not a measuring device) | Copying, enlarging, or reducing plans/maps |
Key Concepts for Students
- Area of irregular figures: The planimeter’s greatest advantage is measuring area of figures that cannot be broken down into standard geometric shapes. Any closed boundary on paper — no matter how irregular — can be traced and its enclosed area found in one operation.
- Volume from planimeter areas: In earthwork calculations, planimeter-measured cross-sectional areas at chainages are combined using the prismoidal formula or average end-area method to compute cut and fill volumes. The planimeter provides the area input; the engineer performs the volume calculation separately.
- Map scale must be known: The planimeter reads area in dial units scaled by M. To get actual ground area, the plan area must be converted using the map’s scale factor: actual area = plan area × (scale ratio)².