Study Material — 8 PYQs (2018–2018) · Concept Notes · Shortcuts
SSC CPO Cylinder, Cone, Sphere is a frequently tested subtopic — 8 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.
A sphere of radius 6 cm is melted and recast into a cylinder of radius 4 cm. What is the height of the cylinder? [Use π = 22/7]
Exam Q 42018Previous Year Pattern
A cone has a base radius of 5 cm and slant height of 13 cm. What is the total surface area of the cone? [Use π = 22/7]
Exam Q 52018Previous Year Pattern
The volume of a sphere is 4851 cm³. What is its radius? [Use π = 22/7]
Exam Q 62018Previous Year Pattern
A solid metallic sphere of radius 6 cm is melted and recast into a solid cone with base radius 4 cm. Find the height of the cone (in cm).
Exam Q 72018Previous Year Pattern
A cone with base radius 6 cm and height 8 cm is filled with water. The water is poured into a sphere of radius 5 cm. What percentage of the sphere's volume will be filled with water?
Exam Q 82018Previous Year Pattern
A cone and a cylinder have equal base radii and equal volumes. If the height of the cylinder is 9 cm, find the height of the cone (in cm).
Concept Notes
Cylinder, Cone, Sphere— Rules & Concept
💡
Core Concept
Read this first — the foundation of the topic
→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
💡Key Formulas 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 Patterns
What 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.
⚡
Shortcuts
Use 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
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
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)