This page covers Agniveer Army CEE Cylinder, Cone, Sphere with complete concept notes, 8 graded practice MCQs, key points and exam-specific tips. Free to study.
Core ConceptRead this first — the foundation of the topic
Cylinder, Cone, and Sphere are the three most important 3D shapes in SSC CGL. These appear in 2-3 questions every year, making them high-scoring topics. Understanding their formulas and relationships is crucial for exam success. Core Concepts:
A Cylinder is like a circular tube - think of a water pipe or tin can. It has two circular ends and a curved surface. A Cone is like an ice cream cone - one circular base and comes to a point at the top.
A Sphere is a perfect ball - like a football or marble.
Formula BlockMemorise — at least one formula appears in every paper
Block:
Cylinder: Volume = πr²h, Curved Surface Area = 2πrh, Total Surface Area = 2πr(r+h)
Cone: Volume = (1/3)πr²h, Curved Surface Area = πrl, Total Surface Area = πr(r+l), where l = √(r²+h²)
Sphere: Volume = (4/3)πr³, Surface Area = 4πr²
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL typically asks: volume calculations (40%), surface area problems (35%), and mixed problems involving two shapes (25%). Questions often involve finding radius, height, or comparing volumes.
ShortcutsUse these to save 30–60 seconds per question
Volume Ratio Trick
Cylinder:Cone:Sphere with same radius and height = 3:1:4 (when sphere diameter = cylinder height)
2
Quick Surface Area
For cylinder, if radius = height, then Total SA = 6πr²
3
Cone Slant Height
Use 3-4-5 triangle ratios when possible
Worked ExampleSolve this step-by-step before moving on
Total SA = 2πr(r+h) = 2 × (22/7) × 7 × (7+10) = 44 × 17 = 748 m²
Worked Example 2:
A cone and sphere have the same radius 6cm. If cone's height is 8cm, find the ratio of their volumes.
Ratio = 96π : 288π = 1:3
Most Common Trap:
Students confuse slant height (l) with actual height (h) in cone problems. Remember: slant height is the distance from base edge to apex, while height is perpendicular distance from base to apex. Always check if the given measurement is l or h before applying formulas.
Another frequent mistake is forgetting to use 'curved surface area' vs 'total surface area'. Read questions carefully - if a cylinder has open ends, use curved surface area only.
Key Points to Remember
Cylinder volume = πr²h, remember to multiply base area by height
Cone volume is exactly 1/3 of cylinder volume with same base and height
Sphere volume formula: (4/3)πr³ - memorize this fraction carefully
Cylinder total surface area = 2πr(r+h) - factor out 2πr for speed
Cone slant height l = √(r²+h²) using Pythagoras theorem
Sphere surface area = 4πr² - exactly 4 times the great circle area
Volume ratio shortcut: Cylinder:Cone:Sphere = 3:1:4 (same r and h)
For cylinder CSA problems, use 2πrh (curved surface only)
Cone total SA = πr(r+l) where l is slant height, not vertical height
Common trap: always distinguish between slant height and vertical height in cones
Exam-Specific Tips
Value of π in SSC calculations is typically 22/7 or 3.14
Volume of cone is always 1/3 times volume of cylinder with same base and height
Sphere has minimum surface area for given volume among all 3D shapes
Hemisphere volume = (2/3)πr³ and surface area = 3πr²
Cylinder with radius = height has total surface area = 6πr²
Cone with base radius = height has slant height = r√2
Volume of sphere inscribed in cube of side 'a' = (π/6)a³
Ratio of volumes of cube to inscribed sphere = 6:π
Practice MCQs
Cylinder, Cone, Sphere — Practice Questions
8graded MCQs · easy to hard · full solution & trap analysis