PYQs
Practise questions grouped by chapter and source year.
Practice questions are organised using the years and labels in our source collection. Work through the solutions with your teacher; these are not a complete official examination paper.
Practice question 1
Source year: 20253 marksCone, hemisphere, cylinder on equal bases. Ratio of volumes. [CBSE 2025]
Practice question 2
Source year: 20243 marksSphere r=4.2cm melted into cylinder r=6cm. Find height. [CBSE 2024]
Practice question 3
Source year: 20253 marksA cone, hemisphere and cylinder stand on equal bases and have same height. Find ratio of their volumes. [CBSE 2025]
Practice question 4
Source year: 20243 marksA metallic sphere of radius 4.2cm is melted and recast into shape of cylinder of radius 6cm. Find height of cylinder. [CBSE 2024]
Practice question 5
Source year: 20233 marksFind volume and surface area of sphere of diameter 14cm. [CBSE 2023]
Practice question 6
Source year: 20223 marksA toy is in form of cone mounted on hemisphere. Radius is 3.5cm and total height is 15.5cm. Find volume. [CBSE 2022]
Formulae
Revisit important relationships and quick revision formulae.
Cylinder Volume
V = πr²h
Cone Volume
V = (1/3)πr²h
Sphere Volume
V = (4/3)πr³
Cuboid
Volume = l×b×h\nTotal Surface Area = 2(lb+bh+hl)\nLateral Surface Area = 2h(l+b)
Cube
Volume = a³\nTotal Surface Area = 6a²\nLateral Surface Area = 4a²
Cylinder
Volume = πr²h\nCurved Surface Area = 2πrh\nTotal Surface Area = 2πr(r+h)
Cone
Volume = (1/3)πr²h\nCurved Surface Area = πrl (l=slant height)\nTotal Surface Area = πr(r+l)\nSlant height: l = √(r²+h²)
Sphere
Volume = (4/3)πr³\nSurface Area = 4πr²
Hemisphere
Volume = (2/3)πr³\nCurved Surface Area = 2πr²\nTotal Surface Area = 3πr²
Derivations
Work through the reasoning behind key concepts.
Volume Conservation
When a solid is melted and recast into different shape, volume remains constant. Volume before melting = Volume after recasting. Use this principle: Find volume of original shape, equate to volume of new shape, solve for unknown dimension.
Volume Conservation
When object is melted and recast: Volume before = Volume after\nUse this to find unknown dimension
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