Study Material — 9 PYQs (2019–2019) · Concept Notes · Shortcuts
IBPS RRB PO Cylinder, Cone, Sphere is a frequently tested subtopic — 9 previous year questions from 2019–2019 papers are included below with concept notes, key rules and shortcut tricks.
IBPS RRB PO Cylinder, Cone, Sphere — Past Exam Questions
9 questions from actual IBPS RRB PO papers · all shown free · click option to reveal solution
Exam Q 12019Previous Year Pattern
The volume of a sphere is 288π cm³. What is its radius (in cm)?
Exam Q 22019Previous Year Pattern
A cone has a base radius of 6 cm and height of 8 cm. What is its slant height (in cm)?
Exam Q 32019Previous Year Pattern
The volume of a cylinder is 1540 cm³ and its height is 10 cm. What is its radius (in cm)?
Exam Q 42019Previous Year Pattern
A cylinder has a total surface area of 352 cm² and radius of 4 cm. What is its height (in cm)?
Exam Q 52019Previous Year Pattern
A cone has a base radius of 6 cm and slant height of 10 cm. What is the ratio of its curved surface area to its total surface area?
Exam Q 62019Previous Year Pattern
A cone is inscribed in a sphere of radius 13 cm such that the base of the cone touches the sphere and the apex is at the centre of the sphere. If the base radius of the cone is 12 cm, what is the height of the cone?
Exam Q 72019Previous Year Pattern
The volume of a cylinder is 1540 cm³ and its height is 10 cm. If a cone with the same base radius and height is formed, what is the ratio of the cylinder's volume to the cone's volume?
Exam Q 82019Previous Year Pattern
A cylinder has a radius of 7 cm and height of 10 cm. If the radius is increased by 50% while the height remains the same, by what percentage does the volume increase?
Exam Q 92019Previous 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).
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
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)