Key facts

  • Rectangle: area = length x breadth and perimeter = 2 x (length + breadth). Convert all lengths into the same unit before calculation.
  • Triangle: area = 1/2 x base x height. The height must be perpendicular to the chosen base; a slant side is not automatically the height.
  • Circle: circumference = 2 x pi x radius and area = pi x radius^2. If diameter is given, first use radius = diameter / 2.
  • Cylinder: curved surface area = 2 x pi x r x h, total surface area = 2 x pi x r x (r + h), and volume = pi x r^2 x h.
  • Sphere: surface area = 4 x pi x r^2 and volume = 4/3 x pi x r^3. All points on a sphere are at the same distance from its centre.

Key Points at a Glance

  1. 1

    Rectangle: area = length x breadth and perimeter = 2 x (length + breadth). Convert all lengths into the same unit before calculation.

  2. 2

    Triangle: area = 1/2 x base x height. The height must be perpendicular to the chosen base; a slant side is not automatically the height.

  3. 3

    Circle: circumference = 2 x pi x radius and area = pi x radius^2. If diameter is given, first use radius = diameter / 2.

  4. 4

    Ellipse: area = pi x semi-major axis x semi-minor axis. If full major and minor axes are given, halve them before using the formula.

  5. 5

    Cylinder: curved surface area = 2 x pi x r x h, total surface area = 2 x pi x r x (r + h), and volume = pi x r^2 x h.

  6. 6

    Sphere: surface area = 4 x pi x r^2 and volume = 4/3 x pi x r^3. All points on a sphere are at the same distance from its centre.

  7. 7

    Cube: volume = side^3 and total surface area = 6 x side^2. For a cube, length, breadth, and height are equal.

  8. 8

    Cone: volume = 1/3 x pi x r^2 x h. Do not confuse vertical height with slant height; volume uses vertical height.

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Mensuration in the CET senior-secondary syllabus

For CET Senior Secondary 2026, this topic belongs to Logical Reasoning and Mathematics. The official scope is narrow and practical: area of triangle, circle, ellipse, rectangle, sphere, and cylinder; and volume of sphere, cylinder, cube, and cone. A useful preparation strategy is therefore to master formula selection, unit conversion, and common traps in two-dimensional and three-dimensional figures.

Mensuration questions usually begin with an everyday situation: fencing, painting, tiling, filling a tank, making a container, or comparing two shapes. The first decision is the type of answer required. Boundary length points to perimeter or circumference. Surface covered points to area or surface area. Capacity or space occupied points to volume. This one decision prevents many wrong options.

Keep the unit logic clear. Length is written in units such as cm or m, area in square units, and volume in cubic units. If a question mixes metres and centimetres, convert first and calculate later.

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