4 questions from actual AFCAT papers · all shown free · click option to reveal solution
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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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
l = square root of (r squared + h squared)
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. ---
CYLINDER
CONE
SPHERE
HEMISPHERE
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Find volume or surface area given r and h. 2
A solid is melted and recast into another shape. Volume stays the same. 3
Compare volumes or surface areas of two shapes. 4
A cone on top of a cylinder, or hemisphere on top of a cylinder. 5
If radius doubles, how does volume change? --- 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
Number of small solids = Volume of big solid / Volume of one small solid Always equate volumes. Never equate surface areas in melting problems
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. ---
Volume of big sphere = (4/3) × pi × 6³ = (4/3) × pi × 216 = 288 pi
Volume of one small sphere = (4/3) × pi × 2³ = (4/3) × pi × 8 = (32/3) pi
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. --- 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)
Slant height of cone l = sqrt(3² + 4²) = sqrt(9+16) = sqrt(25) = 5 cm
Volume of cylinder = pi × 3² × 5 = 45 pi
Volume of cone = (1/3) × pi × 3² × 4 = (1/3) × pi × 36 = 12 pi
Total volume = 45 pi + 12 pi = 57 pi = 57 × 3.14 = 178.98 cm³ Answer: 178.98 cm³ ---
— 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.
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