Study Material — 6 PYQs (2018–2018) · Concept Notes · Shortcuts
SBI Clerk Cylinder, Cone, Sphere is a frequently tested subtopic — 6 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.
SBI Clerk Cylinder, Cone, Sphere — Past Exam Questions
6 questions from actual SBI Clerk papers · all shown free · click option to reveal solution
Exam Q 12018Previous Year Pattern
A cylinder and a cone have the same radius of 5 cm and the same height of 12 cm. What is the ratio of their volumes?
Exam Q 22018Previous Year Pattern
The total surface area of a sphere is 616 cm². What is its radius? (Use π = 22/7)
Exam Q 32018Previous Year Pattern
A cone has a base radius of 8 cm and height of 15 cm. What is its slant height?
Exam Q 42018Previous Year Pattern
The volume of a sphere is 288π cm³. What is its radius?
Exam Q 52018Previous Year Pattern
The curved surface area of a cone is 550 cm² and its slant height is 25 cm. What is the radius of the base of the cone? (Use π = 22/7)
Exam Q 62018Previous Year Pattern
A sphere has a radius of 6 cm. If the radius is increased by 50%, by what percentage does the volume increase? (Use π = 22/7)
Concept Notes
Cylinder, Cone, Sphere— Rules & Concept
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
7graded MCQs · easy to hard · full solution & trap analysis
The total surface area of a sphere is 616 cm². What is the radius of the sphere? (Use π = 22/7)
Practice 2medium
A cone and a cylinder have the same base radius of 5 cm and the same height of 12 cm. What is the ratio of their volumes?
Practice 3hard
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?
Practice 4hard
Two spheres have radii in the ratio 2:3. If the surface area of the smaller sphere is 144π cm², what is the volume of the larger sphere (in cm³)?
Practice 5hard
A cone and a cylinder have equal volumes. The cone has base radius 6 cm and height 15 cm. If the cylinder has the same base radius as the cone, what is the height of the cylinder (in cm)?
Practice 6hard
A hemispherical bowl of radius 10 cm is filled with water. The water is poured into a conical vessel with base radius 5 cm. To what height (in cm) will the water rise in the cone?
Practice 7hard
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).
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)