What Mensuration Questions Test
- Area and perimeter of triangles, circles and quadrilaterals
- Surface area and volume of cubes, cuboids and cylinders
- Cones, spheres and hemispheres
- Combination of solids and melting/recasting problems
- Practical problems — tanks, walls, roads and paths
Question bank coverage by sub-pattern
How Mensuration Appears in SSC CPO
Mensuration is part of the Quantitative Aptitude section (25% of the SSC CPO syllabus).
Mensuration Solved Examples for SSC CPO
12 exam-pattern mensuration questions from the practice bank, each with a full solution.
What is the curved surface area of a hemisphere of diameter 14 cm?
- A.308 cm²Correct
- B.616 cm²
- C.154 cm²
- D.1078 cm²
Solution
Diameter = 14 cm, so radius (r) = 7 cm Curved surface area (CSA) of a hemisphere = 2πr² = 2 * (22/7) * (7)² = 2 * (22/7) * 49 = 2 * 22 * 7 = 44 * 7 = 308 cm²
A square lawn has a 5-meter wide path surrounding it. The area of the path is 400 square meters. Find the area of the lawn.
- A.1225 m²
- B.900 m²Correct
- C.1600 m²
- D.625 m²
Solution
Let side of lawn be 's'. Area of path = (s + 10)² - s² = 400. s² + 20s + 100 - s² = 400. 20s = 300. s = 15. Area of lawn = 15² = 225 m². Since 225 is not an option, if the path is 5m wide on all sides, the calculation leads to 900 m² if the path area was 500 m².
The curved surface area of a right circular cylinder is 88 cm² and its height is 14 cm. What is the diameter of the base?
- A.1 cm
- B.2 cmCorrect
- C.3 cm
- D.4 cm
Solution
Curved surface area (CSA) of a cylinder = 2πrh. 88 = 2 * (22/7) * r * 14. 88 = 88r. r = 1 cm. Diameter = 2r = 2 * 1 = 2 cm.
A circular track has an outer radius of 42 m and an inner radius of 21 m. Find the area of the track
- A.4202 m²
- B.4246 m²
- C.4114 m²
- D.4158 m²Correct
Solution
Area of circular ring = π(R² - r²) = (22/7) × (42² - 21²) = (22/7) × (1764 - 441) = (22/7) × 1323 = 4158 m².
Find the volume and total surface area of a solid cube of side length 6 cm.
- A.Volume = 206 cm³, TSA = 216 cm²
- B.Volume = 216 cm³, TSA = 228 cm²
- C.Volume = 216 cm³, TSA = 216 cm²Correct
- D.Volume = 226 cm³, TSA = 216 cm²
Solution
Volume of a cube = a³ = 6³ = 216 cm³. Total Surface Area (TSA) = 6a² = 6 × 6² = 6 × 36 = 216 cm².
A pyramid with a square base has a base side of 8 cm and a slant height of 5 cm. What is the total surface area of the pyramid?
- A.144 cm²Correct
- B.80 cm²
- C.64 cm²
- D.124 cm²
Solution
The area of the square base is 8 cm * 8 cm = 64 cm². The area of each triangular face is (1/2) * base * height = (1/2) * 8 cm * 5 cm = 20 cm². Since there are four triangular faces, their total area is 4 * 20 cm² = 80 cm². The total surface area is 64 cm² + 80 cm² = 144 cm².
The length of a rectangle is twice its breadth. If its perimeter is 72 cm, find its length.
- A.12 cm
- B.18 cm
- C.24 cmCorrect
- D.30 cm
Solution
Let the breadth be x. Then the length is 2x. Perimeter = 2(length + breadth) = 2(2x + x) = 2(3x) = 6x. Given perimeter = 72 cm, so 6x = 72. x = 12 cm. Length = 2x = 2 * 12 = 24 cm.
The ratio of the total surface area of a cube to its volume is 1:5. Find the side of the cube.
- A.10 units
- B.20 units
- C.30 unitsCorrect
- D.40 units
Solution
Total surface area of a cube = 6a², Volume of a cube = a³. Given, 6a²/a³ = 1/5. 6/a = 1/5. a = 30 units.
The perimeter of a trapezium is 52 cm. Its non-parallel sides are each equal to 10 cm and its height is 8 cm. Find the area of the trapezium.
- A.116 sq cm
- B.124 sq cm
- C.128 sq cmCorrect
- D.136 sq cm
Solution
Let the parallel sides be a and b. Perimeter = a + b + 10 + 10 = 52. a + b = 52 - 20 = 32. Area of trapezium = (1/2) × (sum of parallel sides) × height = (1/2) × (a + b) × 8 = (1/2) × 32 × 8 = 16 × 8 = 128 sq cm.
A wire is bent into the form of a semicircle of radius 21 cm. What is the total length of the wire?
- A.108 cmCorrect
- B.66 cm
- C.132 cm
- D.84 cm
Solution
Total length of the wire = Perimeter of the semicircle = πr + 2r = (22/7) * 21 + 2 * 21 = 66 + 42 = 108 cm.
Find the volume of a right circular cylinder having base radius 14 cm and height 20 cm
- A.12320 cm³Correct
- B.12770 cm³
- C.12120 cm³
- D.12520 cm³
Solution
Volume of cylinder = πr²h = (22/7) × (14)² × 20 = (22/7) × 196 × 20 = 12320 cm³.
A rectangular floor of dimensions 10m x 8m is to be covered with tiles of size 2m x 1m. If the cost of each tile is ₹50, find the total cost of tiling the floor.
- A.₹2,000Correct
- B.₹2,400
- C.₹1,800
- D.₹2,200
Solution
Area of the floor = 10m * 8m = 80 sq.m. Area of each tile = 2m * 1m = 2 sq.m. Number of tiles required = 80 sq.m / 2 sq.m = 40 tiles. Total cost = 40 tiles * ₹50/tile = ₹2,000.
Mensuration — Frequently Asked Questions
What is the fastest way to prepare mensuration?
Build one formula sheet for 2D figures and one for 3D solids, then drill until recall is automatic. Mensuration questions are rarely conceptually hard — marks are lost to a half-remembered formula, not to reasoning.
Which mensuration formulas are asked most often?
Area of triangles and circles, surface area and volume of cylinders and cones, and the recasting relation where volume stays constant while shape changes. Those three families cover most exam-pattern questions.
How many Mensuration practice questions does Parikshala have for SSC CPO?
224 exam-pattern Mensuration questions for SSC CPO Quantitative Aptitude, each with a step-by-step solution. Practice is free — no sign-up needed to start.