Study Material — 4 PYQs (2018–2020) · Concept Notes · Shortcuts
NDA 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.
4 questions from actual NDA papers · all shown free · click option to reveal solution
Exam Q 12020Previous Year Pattern
A solid sphere has a radius of 7 cm. What is the volume of the sphere? (Use π = 22/7)
Exam Q 22018Previous Year Pattern
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 ConceptRead this first — the foundation of the topic
CYLINDER, CONE, SPHERE — COMPLETE GUIDE FOR SSC CGL ---
CORE CONCEPT These three shapes are 3D (solid) figures. Every SSC CGL paper has 2-4 questions from this topic. Questions test your ability to find Volume, Curved Surface Area (CSA), and Total Surface Area (TSA). Sometimes two shapes are combined — like a cone placed on top of a cylinder. Master the formulas and you will never drop marks here.
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Key RulesCore rules you must know cold
Cylinder
Think of a cold drink can. It has two circular faces (top and bottom) and one curved surface around it. Radius = r, Height = h.
Cone: Think of an ice cream cone. It has one circular base and one curved surface tapering to a point.
Radius = r, Height = h, Slant Height = l
Remember
l = square root of (r squared + h squared)
Sphere
Think of a football. It is perfectly round with no flat face. Radius = r. A Hemisphere is exactly half a sphere — it has one curved surface and one flat circular face.
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Formula BlockMemorise — at least one formula appears in every paper
CYLINDER
• Volume = pi × r² × h
• CSA (Lateral Surface) = 2 × pi × r × h
• TSA = 2 × pi × r × (r + h)
CONE
• Slant Height l = sqrt(r² + h²)
• Volume = (1/3) × pi × r² × h
• CSA = pi × r × l
• TSA = pi × r × (r + l)
SPHERE
• Volume = (4/3) × pi × r³
• Surface Area = 4 × pi × r²
HEMISPHERE
• Volume = (2/3) × pi × r³
• CSA = 2 × pi × r²
• TSA = 3 × pi × r²
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Exam PatternsWhat examiners ask — read before attempting PYQs
Direct formula application
Find volume or surface area given r and h.
2
Melting and recasting
A solid is melted and recast into another shape. Volume stays the same.
3
Ratio problems
Compare volumes or surface areas of two shapes.
4
Combined solids
A cone on top of a cylinder, or hemisphere on top of a cylinder.
5
Percentage change
If radius doubles, how does volume change?
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SHORTCUTS AND TRICKS
SHORTCUT 1 — Volume Ratio of Cone : Cylinder : Sphere (same r, same h where h = 2r for sphere):
Cone : Cylinder : Sphere = 1 : 3 : 2
This is a golden ratio. If the exam gives you same base and height, use this directly
SHORTCUT 2 — Melting and Recasting Formula
Number of small solids = Volume of big solid / Volume of one small solid
Always equate volumes. Never equate surface areas in melting problems
SHORTCUT 3 — Effect of Radius Change on Volume
Volume is proportional to r². If radius becomes n times, volume becomes n² times (for cylinder with same h). For sphere, volume becomes n³ times since it depends on r³.
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Worked ExampleSolve this step-by-step before moving on
1
Step 1
Volume of big sphere = (4/3) × pi × 6³ = (4/3) × pi × 216 = 288 pi
2
Step 2
Volume of one small sphere = (4/3) × pi × 2³ = (4/3) × pi × 8 = (32/3) pi
3
Step 3
Number of spheres = 288 pi ÷ (32/3) pi = 288 × 3/32 = 864/32 = 27
Answer: 27 small spheres.
Key insight: pi cancels out. Always cancel pi before calculating — saves time.
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WORKED EXAMPLE 2 — Combined Solid
Question: A toy is made of a cone on top of a cylinder. Cylinder has r = 3 cm, h = 5 cm. Cone has same r = 3 cm, h = 4 cm. Find total volume. (Use pi = 3.14)
1
Step 1
Slant height of cone l = sqrt(3² + 4²) = sqrt(9+16) = sqrt(25) = 5 cm
2
Step 2
Volume of cylinder = pi × 3² × 5 = 45 pi
3
Step 3
Volume of cone = (1/3) × pi × 3² × 4 = (1/3) × pi × 36 = 12 pi
4
Step 4
Total volume = 45 pi + 12 pi = 57 pi = 57 × 3.14 = 178.98 cm³
Answer: 178.98 cm³
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Exam TrapsCommon mistakes students make — avoid these
— THE NUMBER 1 TRAP
Students confuse CSA and TSA. In problems asking for the cost of painting the OUTSIDE of a container that is open at the top — use CSA of the curved part + area of the base only. Do NOT add the top circle.
Read the question carefully. Also, many students forget to calculate slant height l before finding cone's surface area — they use h instead of l in the formula pi × r × l. This gives a completely wrong answer.
Key Points to Remember
Volume of Cylinder = pi × r² × h; TSA = 2 × pi × r × (r + h)
Volume of Cone = (1/3) × pi × r² × h — exactly one-third of cylinder with same base and height
Slant height of Cone: l = sqrt(r² + h²) — always calculate l before finding cone's surface area
Volume of Sphere = (4/3) × pi × r³; Surface Area = 4 × pi × r²
Hemisphere TSA = 3 × pi × r² (curved surface + one flat circular base)
Golden Ratio — Cone : Cylinder : Sphere volumes = 1 : 3 : 2 when base radius and relevant height are equal
In melting/recasting problems, always equate VOLUMES — surface area does not stay the same
If radius is doubled, cylinder volume becomes 4 times; sphere volume becomes 8 times
Number of small solids formed = Volume of large solid divided by volume of one small solid
For open containers, use CSA (not TSA) — do not include the open face in surface area
Exam-Specific Tips
Volume of a cone is exactly 1/3rd of the volume of a cylinder with the same base radius and height
The slant height formula for a cone is l = sqrt(r² + h²) — this appears directly in MCQs
Surface area of a sphere = 4 × pi × r², which equals the lateral surface area of a cylinder with height 2r and same radius
TSA of hemisphere = 3 × pi × r²; CSA of hemisphere = 2 × pi × r²
If a solid sphere of radius R is melted into small spheres of radius r, number of spheres = (R/r)³
Volume ratio of Cone : Cylinder : Sphere with same base and height (h = 2r for sphere) = 1 : 3 : 2
For a cylinder, if height is doubled and radius is halved, volume becomes half the original
Total Surface Area of a cone = pi × r × (r + l), where l is slant height — NOT vertical height h
Practice MCQs
Cylinder, Cone, Sphere — Practice Questions
36graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 36
A sphere has a radius of 7 cm. What is its surface area (in cm²)?
Practice 2easy
A cone has a base radius of 7 cm and height of 6 cm. What is its volume? (Use π = 22/7)
Practice 3easy
The volume of a sphere is 288π cm³. What is its radius?
Practice 4easy
A cylinder has a volume of 1540 cm³ and height of 10 cm. What is its radius? (Use π = 22/7)
Practice 5easy
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 6easy
A cylinder has a total surface area of 462 cm² and radius 7 cm. What is its height?
Practice 7easy
A sphere has a surface area of 616 cm². What is its radius? (Use π = 22/7)
Practice 8easy
The volume of a sphere is 288π cm³. What is its radius?
Practice 9easy
The total surface area of a sphere is 616 cm². What is its radius? (Use π = 22/7)
Practice 10easy
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 11easy
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 12medium
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 13medium
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 14medium
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 15medium
A sphere has a radius of 6 cm. If the radius is increased by 50%, what is the percentage increase in its volume?
Practice 16medium
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 remaining volume (in cm³)?
Practice 17medium
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 18medium
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)?
Practice 19medium
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 20medium
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?
16 more practice questions in the Study Panel
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