8 questions from actual SSC CPO papers · all shown free · click option to reveal solution
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.
Block:
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.
Cylinder:Cone:Sphere with same radius and height = 3:1:4 (when sphere diameter = cylinder height) 2
For cylinder, if radius = height, then Total SA = 6πr² 3
Use 3-4-5 triangle ratios when possible
Volume = πr²h = (22/7) × 7² × 10 = (22/7) × 49 × 10 = 22 × 7 × 10 = 1540 m³
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.
Cone volume = (1/3)πr²h = (1/3) × π × 6² × 8 = 96π cm³
Sphere volume = (4/3)πr³ = (4/3) × π × 6³ = (4/3) × π × 216 = 288π cm³
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.