- Chapter scope (2026-27 book): only 2 exercises — 12.1 (Surface Area of Combination of Solids), 12.2 (Volume of Combination of Solids). No Exercise 12.3.
- Golden rule for combination surface area: when two solids are joined, the surface where they meet is hidden — never add both solids’ full surface areas; add only the curved/visible parts.
- Golden rule for combination volume: volumes simply add (or subtract, for carved-out cavities) — no hidden-surface adjustment needed for volume.
- Cube: TSA = 6a², Volume = a³
- Cuboid: TSA = 2(lb+bh+hl), Volume = lbh
- Cylinder: CSA = 2πrh, TSA = 2πr(r+h), Volume = πr²h
- Cone: CSA = πrl, TSA = πr(l+r), Volume = (1/3)πr²h, where l = √(r²+h²)
- Sphere: SA = 4πr², Volume = (4/3)πr³
- Hemisphere: CSA = 2πr², TSA = 3πr², Volume = (2/3)πr³
- Cone + hemisphere (same radius) toy: TSA = πr(l+2r); Volume = (1/3)πr²h + (2/3)πr³
- Cylinder + 2 hemispheres (capsule): TSA = 2πr(h_cyl+2r); Volume = πr²h_cyl + (4/3)πr³
- Cylinder with a cone hollowed out: TSA = CSA(cylinder) + base circle + CSA(cone); Volume = Volume(cylinder) − Volume(cone)
- Melting-and-recasting problems: always conserve volume, never surface area, when reshaping one solid into another.
- Common error to avoid: forgetting to subtract 2r (diameter) from total height when a hemisphere/sphere is attached at both ends of a cylinder, before computing the cylinder’s own height.
See the full Solutions post · Extra Questions / HOTS · Class 10 Maths Formulas Handbook
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