Mensuration Tests — Pick a Level and Start
Tap a level to see every test in it. Level 1 is set at real SSC CGL difficulty — start there the day you finish the formulas. Level 2 is pitched above the exam, to push accuracy under pressure.
Level 1 SSC CGL Level Checking… View tests
Same difficulty as the real SSC CGL paper — one formula applied cleanly. The surface, volume and diagonal of cubes and cuboids; a box from its three face areas; bricks in a wall; the rise in a tank; what happens when edges or radii are scaled; the curved surface, total surface and volume of a cylinder, a pipe and a cone; tents and canvas; the frustum and the bucket; spheres, hemispheres and bowls; prisms and pyramids; toys made of two or three solids; a sphere in a cube or a cone in a cylinder; the rise when a ball is dropped in; melting into balls, wires and cones; cutting and painting cubes; wells and embankments; Euler's formula; flow through a pipe; and sectors, rings, paths and wheels. A steady score here means the chapter is exam-ready.
Level 2 Above SSC CGL Level Checking… View tests
Harder than the exam asks, because every question chains two steps or runs one backwards. A room's height from its volume, then its longest pole; a cylinder whose radius and height add up to a given number; a hollow sphere from the steel it uses; a cone cut into equal volumes; the largest cube inside a sphere, then cut into smaller cubes; a ball resting in a cone with water that just covers it; a hemisphere recast into a cylinder of a given surface ratio; three balls from one; a painted cube counted by faces; a pyramid's height from the water it pushes up; a cistern's draining time; and a tethered horse's ungrazed field. Clear these and the real paper feels easy.
A mensuration question is a formula waiting to be picked. Once you know which solid the question is about — a cylinder, a cone, a frustum, a hemisphere, or two of them joined — the working is usually two lines. The skill is naming the solid and the quantity before you calculate: curved surface or total surface, volume or capacity, the outer radius or the inner one.
The marks are lost in three places. The first is using the height where the slant height is needed — a cone's or frustum's curved surface needs l, not h. The second is counting the wrong surfaces: an open bucket has no top, a pipe has no ends, and joining two solids hides the faces that touch. The third is mixing units — centimetres with metres, litres with cubic centimetres. Each test puts twenty-five mensuration questions in front of you in one sitting, which is what makes those checks automatic.
How Many Mensuration Questions Are Asked in SSC CGL?
Mensuration is a regular part of advanced maths. Tier I usually has two or three questions and Tier II has a few more, most of them on the cylinder, cone, sphere and frustum, or on melting one solid into another.
| Chapter | Tier I (out of 25) | Tier II Paper I (out of 30) |
|---|---|---|
| Mensuration (areas and volumes) | 2–3 | 3–4 |
| Geometry (triangles, quadrilaterals, circles) | 2–3 | 3–5 |
Counts vary by shift. Geometry supplies the lengths and right triangles that mensuration questions start from, so the two chapters are best prepared back to back.
What You Will Practice in the Mensuration Chapter
Cubes, cuboids and prisms
- Surface area, volume and diagonal of cubes and cuboids, and a box from its three face areas
- Rooms, walls and painting costs; bricks, tiles and boxes packed into a space
- Tanks, rainfall and the rise in water level
- Prisms and pyramids on square, triangular, hexagonal and trapezium bases
- Scaling — what happens to surface and volume when edges change
Cylinders, cones, frustums and spheres
- Cylinders and hollow cylinders — curved surface, total surface, volume and metal used
- Cones and tents — slant height, canvas, and the cone formed by turning a right triangle
- Frustums — buckets, lampshades and a cone cut by a plane parallel to its base
- Spheres, hemispheres and hollow bowls
- Combined solids — capsules, toys, tents and ice-cream cones
Changing one solid into another
- Melting and recasting into balls, wires, cones and bullets
- Water displacement — balls, marbles and pyramids dropped into vessels
- Solids inside solids — the largest sphere, cone or cylinder that fits
- Cutting, painting and removing parts — painted cubes, holes and cavities
- Wells and embankments, flow through pipes and canals, and Euler's formula
- 2D work — sectors, segments, rings, paths, fencing and wheel revolutions
Formulas worth memorising
| Solid | Surface | Volume |
|---|---|---|
| Cube of edge a | 6a², diagonal a√3 | a³ |
| Cuboid l × b × h | 2(lb + bh + hl), diagonal √(l² + b² + h²) | lbh |
| Cylinder | curved 2πrh, total 2πr(r + h) | πr²h |
| Hollow cylinder (R, r) | outer + inner + two rings | π(R² − r²)h |
| Cone | curved πrl, l = √(r² + h²) | ⅓πr²h |
| Frustum (R, r) | curved π(R + r)l | ⅓πh(R² + r² + Rr) |
| Sphere | 4πr² | ⁴⁄₃πr³ |
| Hemisphere | curved 2πr², total 3πr² | ⅔πr³ |
| Prism / pyramid | lateral = base perimeter × height (prism) | base × h / ⅓ base × h |
| Scaling every length by k | × k² | × k³ |
| Sector of angle θ | arc (θ/360) × 2πr | area (θ/360) × πr² |
| Polyhedron (Euler) | F + V − E = 2 | |
The cylinder, cone and sphere rows cover most Tier I questions. Melting and recasting only needs the volume column, because volume is kept while surface changes.
The three mistakes that cost the most marks
- Height in place of slant height. The curved surface of a cone or frustum needs
l. With radius 7 and height 24, the slant is 25 — using 24 gives a wrong option that is always there. - Wrong set of surfaces. Open tanks and buckets have no top, pipes have no ends, and a hemisphere on a cylinder hides the circle where they join. List the faces before adding them.
- Mixed units. 1 m³ = 1000 litres and 1 litre = 1000 cm³. Convert every length to one unit before multiplying.
Solved Examples — SSC CGL Mensuration Questions
l = √(7² + 24²) = 25 cm. Curved surface = πrl = 22/7 × 7 × 25 = 550 cm². Using the height 24 instead of 25 gives 528, a trap option. Answer: 550 cm²⁴⁄₃π × 216 = π × 16 × h, so 288 = 16h and h = 18 cm. The π cancels, so no value of π is needed. Answer: 18 cmπ × 36 × h = ⁴⁄₃π × 27 = 36π, so h = 1 cm. Answer: 1 cmV = ⅓πh(R² + r² + Rr) = ⅓ × 22/7 × 6 × (196 + 49 + 98) = 44/7 × 343 = 2156 cm³. Answer: 2156 cm³How the Mensuration Chapter Tests Work
- 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
- Five figure questions in every test, each with an original diagram shown beside the question.
- Optional 15-minute timer — with the clock to build exam speed, without it while you are still learning the chapter.
- Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
- Solutions, shortcut tricks and concept notes open after you submit, question by question.
- English and हिंदी, chosen at the start of every test.
- Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.
How to Prepare Mensuration for SSC CGL
- Learn the formulas in families. Cylinder, cone and hemisphere on the same base and height hold volumes in the ratio 3 : 1 : 2. Memorise them side by side, not one at a time.
- Write down r, h and l first. Most questions give two of them; the third comes from a right triangle before any area or volume.
- Know the slant-height triples. 3-4-5, 5-12-13, 7-24-25, 8-15-17 and 20-21-29 turn most cone and frustum questions into one line.
- Keep volume for recasting. When one solid becomes another, equate volumes and let π and ⁴⁄₃ cancel; never equate surfaces.
- Scale with powers. Lengths × k, surfaces × k², volumes × k³ — and for partial changes, multiply the separate factors.
- List the visible faces. For joined, cut or hollowed solids, count what is added (new cut faces, inner walls) and what disappears (joined faces, holes).
- Convert units at the start. Put every length in the same unit, and remember 1 m³ = 1000 litres.
- Estimate before choosing an option. πr²h with r = 7 and h = 10 is about 1540 — a quick estimate rules out two options.
- Do Level 1 untimed, the same day you finish the theory. It is set at real SSC CGL difficulty; the aim is picking the right formula, not speed.
- Repeat Level 1 with the 15-minute clock on, then move to Level 2. After that, verify against a previous year paper and a full mock test under locked sectional timing.
All SSC CGL Chapter Wise Tests
Every chapter below has its own free Level 1 and Level 2 tests with full solutions.
Browse all 45 chapter tests — Maths (35) · Reasoning (10)
- Number System
- Rule of Divisibility
- Remainder Theorem
- Decimal & Fraction
- LCM & HCF
- Square & Cube Root
- Number Series (AP & GP)
- Power, Indices & Surds
- Algebraic Formula
- Algebraic Result
- Algebraic Expression & Identities
- Percentage
- Profit & Loss
- Discount & Marked Price
- Simple Interest
- Compound Interest
- Ratio & Proportion
- Partnership
- Average
- Problems on Ages
- Mixture & Alligation
- Time & Work
- Pipe and Cistern
- Time, Speed and Distance
- Quadratic Equation
- Boat and Stream
- Races
- Trigonometry
- Heights & Distances
- Geometry
- Mensuration
- Coordinate Geometry
- Probability
- Statistics
- Data Interpretation
- All Maths chapters →
SSC CGL क्षेत्रमिति (Mensuration) चैप्टर टेस्ट — हिंदी में
क्षेत्रमिति का हर प्रश्न सही सूत्र चुनने का खेल है। पहले पहचानें कि प्रश्न किस ठोस के बारे में है — बेलन (CYLINDER), शंकु (CONE), छिन्नक (FRUSTUM), गोला (SPHERE), अर्धगोला (HEMISPHERE) या दो ठोसों का जोड़ — और क्या पूछा है: वक्र पृष्ठ (CURVED SURFACE), कुल पृष्ठ (TOTAL SURFACE) या आयतन (VOLUME)। फिर हल अक्सर दो पंक्तियों का होता है।
अंक तीन जगह कटते हैं। पहली: तिर्यक ऊँचाई (SLANT HEIGHT) की जगह ऊँचाई लेना — शंकु और छिन्नक के वक्र पृष्ठ में l चाहिए, h नहीं। दूसरी: गलत सतहें गिनना — खुली बाल्टी का ढक्कन नहीं होता और जुड़े ठोसों की मिली हुई सतह छिप जाती है। तीसरी: इकाइयाँ मिला देना — 1 m³ = 1000 लीटर। पिघलाकर दूसरा ठोस बनाने (MELTING AND RECASTING) में हमेशा आयतन बराबर रखें, पृष्ठ नहीं।
TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, आकृतियाँ, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (SSC CGL के स्तर का) और लेवल 2 (SSC CGL से कठिन)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 15 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।