RRB Group D Cylinder, Cone, Sphere — Study Material & 3 Practice MCQs | ZestExam
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RRB Group D Cylinder, Cone, Sphere
Study Material · Concept Notes · Shortcuts
This page covers RRB Group D Cylinder, Cone, Sphere with complete concept notes, 3 graded practice MCQs, key points and exam-specific tips. Free to study.
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
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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.
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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.
A solid sphere has a radius of 7 cm. What is the volume of the sphere? (Use π = 22/7)
Practice 2medium
A solid cone has a base radius of 7 cm and a height of 24 cm. A sphere of radius 7 cm is placed inside the cone such that it touches the base and the lateral surface of the cone. What is the volume of the cone that remains after the sphere is removed? (Use π = 22/7)
Practice 3hard
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, find h. (Use π = 22/7)
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)