Mensuration Questions for SSC MTS

Rectangle and Square

These are the most basic shapes tested. A rectangle has two pairs of equal sides (length L and breadth B). A square is a special rectangle where all four sides are equal. Most questions ask for area when perimeter is given or vice versa, or ask you to find the side when area is given.

• Area of Rectangle = L x B
• Perimeter of Rectangle = 2(L + B)
• Area of Square = side x side = s squared
• Perimeter of Square = 4s
• Diagonal of Rectangle = square root of (L squared + B squared)
• Diagonal of Square = s x root 2, approximately 1.414 x s

Triangle

Triangle questions in SSC MTS mostly involve equilateral triangles or right triangles. For a right triangle, area = half x base x height. For equilateral triangles, two formulas are must-know. The Heron formula appears occasionally when all three sides are given.

• Area of any triangle = half x base x height
• Area of equilateral triangle = (root3 / 4) x side squared
• Perimeter of equilateral triangle = 3 x side
• Heron formula: Area = root of s(s-a)(s-b)(s-c) where s = (a+b+c)/2
• For right triangle: hypotenuse squared = base squared + height squared (Pythagoras)

Circle

Circle questions are very frequent. You must know area and circumference cold. SSC MTS also loves questions about rings (two concentric circles) where you subtract the inner area from the outer. Use pi = 22/7 for most calculations unless told otherwise.

• Area of Circle = pi x r squared
• Circumference = 2 x pi x r = pi x d
• Area of ring = pi x (R squared - r squared) where R is outer and r is inner radius
• Use pi = 22/7 in calculations, or pi = 3.14 when the question specifies
• Diameter = 2 x radius; never mix the two up

Cube and Cuboid

Cube is a box where all sides are equal. Cuboid has different length, breadth, and height. Questions ask for total surface area (all 6 faces), lateral surface area (4 side faces only), or volume. Painting problems usually test lateral or total surface area.

• Volume of Cube = side cubed (s3)
• Total Surface Area of Cube = 6 x s squared
• Volume of Cuboid = L x B x H
• Total Surface Area of Cuboid = 2(LB + BH + LH)
• Lateral Surface Area of Cuboid = 2H(L + B)
• Diagonal of Cuboid = root(L squared + B squared + H squared)

Cylinder, Cone, and Sphere

Cylinder and cone are high-frequency 3D shapes in SSC MTS. A cylinder is like a round pillar. A cone is like an ice-cream cone. Sphere is a ball. Focus on volume and curved surface area. For cone, slant height (l) = root(r squared + h squared) is critical.

• Cylinder Volume = pi x r squared x h
• Cylinder CSA (curved surface) = 2 x pi x r x h
• Cylinder TSA = 2 x pi x r x (r + h)
• Cone Volume = (1/3) x pi x r squared x h
• Cone CSA = pi x r x l, where l = root(r squared + h squared)
• Sphere Volume = (4/3) x pi x r cubed; Surface Area = 4 x pi x r squared

• Confusing radius and diameter in circle problems — if the question says diameter is 14, use radius 7, not 14, in the formula.
• Using the slant height of a cone as the height in the volume formula — volume uses vertical height h, not slant height l.
• Forgetting to square the side in area formulas — writing Area = s instead of s squared for a square is a very common slip.
• Mixing up Curved Surface Area (CSA) and Total Surface Area (TSA) — if the question says painting a cylindrical tank open at top, use CSA plus one circle, not full TSA.
• Unit conversion errors — if dimensions are in metres but answer is asked in square centimetres, multiply by 10000 (1 sq m = 10000 sq cm).

• CAVE for Cylinder: CSA = 2pirh, Area total = 2pir(r+h), Volume = pir squared h, Ends are 2 circles.
• Think of a cone as one-third of a cylinder with the same base and height — that is literally what the volume formula means.
• For the ring area, think of it as the big pizza minus the hole in the middle: pi R squared minus pi r squared.
• Slant-height trick for cone: it is always the hypotenuse of a right triangle with legs r and h. Draw a small right triangle to remember it.

• SSC MTS typically puts 1 circle question, 1 rectangle or square question, and 1 cylinder or cone question per paper. Do not skip any of these three.
• Questions are straightforward formula-apply at this level — there are almost no twisted word problems. If you know the formula, you get the mark.
• Memorise root3 = 1.732 and root2 = 1.414 because equilateral triangle and square diagonal questions may ask for decimal answers.
• In previous year papers, recasting problems appear occasionally — a sphere melted into a cylinder. Set volumes equal and solve for the unknown dimension.
• Time target: mensuration questions should be solved in under 60 seconds each. If you need more time, you are probably not remembering the formula and are deriving it — that must be avoided.