Geometry, Mensuration & Data Interpretation Graphs
“Area, perimeter, solid volumes, angle properties, bar charts, line graphs, and pie chart angle fractions.”
1.Visual Data Synthesis and Geometric Theorems
§ 2.1.Data Interpretation (DI) in GATE questions tests fast extraction and mental arithmetic from tabular and graphic presentations.
Pie Chart Mechanics: A full circle spans 360 degrees, representing 100% of the aggregate quantity. Each slice theta represents a fraction theta / 360. If slice angle is 54 degrees, its percentage share is (54 / 360) * 100 = 15%.
Polygon Angle Rules:
- Sum of interior angles of an n-sided polygon = (n - 2) * 180 degrees.
- Sum of exterior angles of ANY convex polygon is ALWAYS 360 degrees.
- Number of diagonals in an n-gon = n*(n - 3) / 2.
Never compute full 4-digit long divisions in GATE DI. Round numbers to 2 significant digits (e.g. 4831 / 9712 ≈ 48 / 97 ≈ 50%) to verify multiple-choice options in seconds.
2. Worked Problem: Cylinder Volume to Wire Conversion
Ensure all units are converted to the same dimension (meters vs millimeters) before equating volumes.
Problem [Original Practice Problem · Modeled on GATE Pattern]:
A solid metallic cylinder of base radius 6 cm and height 12 cm is melted and recast into a uniform cylindrical wire of diameter 2 mm.
What is the total length of the recast wire in meters?
Step 1: Convert all dimensions to centimeters:
Cylinder: R = 6 cm, H = 12 cm.
Wire diameter = 2 mm => radius r = 1 mm = 0.1 cm.
Step 2: Equate conservation of volume (Volume_cylinder = Volume_wire):
pi R^2 H = pi r^2 L
R^2 H = r^2 L
Step 3: Solve for wire length L:
(6)^2 12 = (0.1)^2 L
36 12 = 0.01 L
432 = 0.01 * L => L = 432 / 0.01 = 43,200 cm.
Step 4: Convert length to meters:
L = 43,200 / 100 = 432 meters.
Primary Academic References & Exam Sources
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