SSC GD Constable Cylinder, Cone, Sphere — Study Material, 12 PYQs & Practice MCQs | ZestExam
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SSC GD Constable Cylinder, Cone, Sphere
Study Material — 12 PYQs (2018–2018) · Concept Notes · Shortcuts
SSC GD Constable Cylinder, Cone, Sphere is a frequently tested subtopic — 12 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.
A cylindrical tank has a radius of 5 m and height of 14 m. How many litres of water can it hold? (Use π = 22/7; 1 m³ = 1000 litres)
Exam Q 42018Previous Year Pattern
A cone is formed by rolling a sector of a circle with radius 10 cm and sector angle 216°. What is the radius of the base of the cone?
Exam Q 52018Previous Year Pattern
Two spheres have radii in the ratio 2:3. What is the ratio of their volumes?
Exam Q 62018Previous Year Pattern
A sphere has a radius of 6 cm. What is the ratio of the surface area of the sphere to its volume?
Exam Q 72018Previous Year Pattern
A solid cylinder has radius 7 cm and height 10 cm. If a cone with the same radius and height is removed from the top, what is the volume of the remaining solid (in cm³)?
Exam Q 82018Previous Year Pattern
A cylindrical tank has radius 7 m and height 10 m. Water fills it to a height of 8 m. A solid sphere of radius 3 m is completely submerged in the water. By how much does the water level rise (in metres)?
Exam Q 92018Previous Year Pattern
Two cones have the same height of 12 cm. The first cone has base radius 4 cm and the second has base radius 6 cm. If both cones are melted and recast into a single sphere, what is the radius of the sphere (in cm)?
Exam Q 102018Previous 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 112018Previous Year Pattern
A cone has base radius 5 cm and slant height 13 cm. If the cone is cut by a plane parallel to the base at a height of 6 cm from the apex, what is the volume of the smaller cone (top part) that is removed (in cm³)?
Exam Q 122018Previous Year Pattern
A cone with base radius 8 cm and height 15 cm is placed upside down in a cylindrical container of radius 10 cm and height 20 cm. The container is filled with water up to the brim. What is the volume of water in the container (in cm³)?
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
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)