AFCAT Cylinder, Cone, Sphere — Study Material, 4 PYQs & Practice MCQs | ZestExam
ZestExam
AFCAT Cylinder, Cone, Sphere
Study Material — 4 PYQs (2018–2020) · Concept Notes · Shortcuts
AFCAT Cylinder, Cone, Sphere is a frequently tested subtopic — 4 previous year questions from 2018–2020 papers are included below with concept notes, key rules and shortcut tricks.
A solid cylinder has radius 7 cm and height 20 cm. It is melted and recast into a solid cone of the same radius. What is the height of the cone?
Exam Q 32020Previous Year Pattern
A solid metallic sphere of radius 6 cm is melted and recast into a solid cone with base radius 4 cm. If the height of the cone is h cm, and a cylindrical hole of radius 2 cm and height h cm is drilled through the cone's axis, find the volume of the remaining solid (in cm³).
Exam Q 42018Previous Year Pattern
A solid cone and a solid sphere have the same radius. The height of the cone equals the diameter of the sphere. If the volume of the cone is 72π cm³, what is the volume of the sphere (in cm³)?
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
Practice MCQs
Cylinder, Cone, Sphere — Practice Questions
36graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 36
A sphere has a surface area of 616 cm². What is its radius? (Use π = 22/7)
Practice 2easy
A cylinder has a volume of 1540 cm³ and a height of 10 cm. What is its radius (in cm)? [Use π = 22/7]
Practice 3easy
A sphere has a radius of 7 cm. What is its surface area (in cm²)?
Practice 4easy
A cone has a base radius of 7 cm and height of 6 cm. What is its volume? (Use π = 22/7)
Practice 5easy
A cylinder has a volume of 1540 cm³ and height of 10 cm. What is its radius? (Use π = 22/7)
Practice 6easy
The volume of a cone is 616 cm³ and its height is 12 cm. What is the radius of its base? (Use π = 22/7)
Practice 7easy
A cylinder has a total surface area of 462 cm² and radius 7 cm. What is its height?
Practice 8easy
A cylinder and a cone have the same base radius of 5 cm and the same height of 12 cm. What is the ratio of their volumes?
Practice 9easy
The total surface area of a sphere is 616 cm². What is its radius? (Use π = 22/7)
Practice 10easy
The volume of a sphere is 288π cm³. What is its radius?
Practice 11easy
The volume of a sphere is 288π cm³. What is its radius?
Practice 12medium
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 13medium
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 14medium
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?
Practice 15medium
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 16medium
A cone and a sphere have equal volumes. The cone has radius 6 cm and height 8 cm. What is the radius of the sphere (in cm)?
Practice 17medium
A cone has a base radius of 5 cm and height of 12 cm. If the slant height is increased by 20% while keeping the base radius constant, what is the percentage increase in curved surface area?
Practice 18medium
A solid cone has base radius 5 cm and height 12 cm. It is placed inside a cylinder of the same radius and height. What percentage of the cylinder's volume is NOT occupied by the cone?
Practice 19medium
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).
Practice 20medium
A cylinder has a radius of 7 cm and height of 10 cm. A cone with the same radius and height is placed inside it. What is the difference between their volumes (in cm³)?
16 more practice questions in the Study Panel
Difficulty-graded, bookmarkable, with timed mode. Free account — no credit card.