This page covers RRB Group D Cylinder, Cone, Sphere with complete concept notes, 3 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
3graded MCQs · easy to hard · full solution & trap analysis
A solid sphere has a radius of 7 cm. What is the volume of the sphere? (Use π = 22/7)
Practice 2medium
A solid cone has a base radius of 7 cm and a height of 24 cm. A sphere of radius 7 cm is placed inside the cone such that it touches the base and the lateral surface of the cone. What is the volume of the cone that remains after the sphere is removed? (Use π = 22/7)
Practice 3hard
A solid metallic sphere of radius 6 cm is melted and recast into a solid cone with base radius 4 cm. If the height of the cone is h cm, find h. (Use π = 22/7)
60-Second Revision — Cylinder, Cone, Sphere
Remember: Cone volume = (1/3) × Cylinder volume for same base and height
Formula check: Sphere SA = 4πr², Volume = (4/3)πr³
Trap: Distinguish cone's slant height (l) from vertical height (h)