Study Material — 3 PYQs (2018–2018) · Concept Notes · Shortcuts
SSC CHSL Cylinder, Cone, Sphere is a frequently tested subtopic — 3 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.
A solid metallic sphere of radius 6 cm is melted and recast into a solid cylinder of radius 4 cm. Find the height of the cylinder (in cm).
Exam Q 32018Previous Year Pattern
A solid metallic cylinder of radius 6 cm and height 28 cm is melted and recast into small solid cones, each of radius 2 cm and height 3 cm. How many such cones are formed?
Concept Notes
Cylinder, Cone, Sphere— Rules & Concept
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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
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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.
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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
Practice MCQs
Cylinder, Cone, Sphere — Practice Questions
13graded MCQs · easy to hard · full solution & trap analysis
The curved surface area of a cone is 550 cm² and its slant height is 25 cm. Find the radius of the base of the cone.
Practice 2medium
A solid sphere of radius 5 cm is melted and recast into a cone with base radius 5 cm. What is the height of the cone (in cm)?
Practice 3medium
A sphere has a radius of 6 cm. If the radius is increased by 50%, what is the percentage increase in surface area?
Practice 4medium
The curved surface area of a cone is 550 cm². If the slant height is 25 cm, what is the radius of the base (in cm)?
Practice 5medium
A sphere has a surface area of 616 cm². What is the volume of the sphere? (Use π = 22/7)
Practice 6medium
A solid cylinder has radius 7 cm and height 10 cm. A cone with the same radius and height is carved out from the top. What is the volume of the remaining solid (in cm³)?
Practice 7medium
A cylinder has a radius of 7 cm and height of 10 cm. A cone with the same base radius and height is carved out from it. What is the volume of the remaining solid (in cm³)?
Practice 8hard
The curved surface area of a cone is 60π cm². If the slant height is 10 cm, find the radius of the base. Then, if a sphere of radius equal to this base radius is inscribed in the cone, what is the volume of the sphere (in cm³)?
Practice 9hard
A hollow sphere has an outer radius of 10 cm and inner radius of 8 cm. What is the volume of the material used (in cm³)?
Practice 10hard
A sphere of radius 6 cm is melted and recast into a cylinder of radius 4 cm. What is the height of the cylinder (in cm)?
Practice 11hard
A solid cylinder has radius 7 cm and height 10 cm. A cone with the same base radius and height is carved out from the top. What is the volume of the remaining solid (in cm³)?
Practice 12hard
The volume of a cylinder is 1540 cm³ and its height is 10 cm. A cone with the same radius and height is formed. If the cone's volume is poured into the cylinder, how many times can it be poured before the cylinder overflows (considering the cylinder is initially empty)?
Practice 13hard
A cylinder has radius 5 cm and height 12 cm. A cone with the same base radius and height is carved out from the top. What is the ratio of the remaining volume to the original cylinder volume?
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)