12
CBSE Marks
★★★★★
Difficulty
9
Topics
Very High
Board Weight
Topics Covered
9 key topics in this chapter
Cube, Cuboid, Cylinder: Revision
Cone: CSA, TSA, Volume
Sphere & Hemisphere: SA, Volume
Combination of Solids
Frustum of a Cone
CSA & Volume of Frustum
Conversion of Solids
Melting & Recasting
Real-Life Applications
Study Resources
Key Formulas
| Formula / Rule | Expression |
|---|---|
| Cylinder CSA | \(2πrh\) |
| Cylinder TSA | \(2πr(h+r)\) |
| Cone CSA | \(πrl (l = slant height = √(r²+h²))\) |
| Cone Volume | \(⅓πr²h\) |
| Sphere SA | \(4πr²\) |
| Sphere Volume | \(⁴⁄₃πr³\) |
| Hemisphere CSA | \(2πr²\) |
| Hemisphere TSA | \(3πr²\) |
| Frustum CSA | \(π(r₁+r₂)l (l = √[h²+(r₁−r₂)²])\) |
| Frustum Volume | \(πh/3·(r₁²+r₂²+r₁r₂)\) |
Important Points to Remember
For a combination of solids, add the surface areas of visible faces only — do not add hidden/joined areas.
For volume of a combination, simply add the volumes of all constituent solids.
Frustum: formed by cutting a cone with a plane parallel to its base.
When a solid is melted and recast, volume is conserved (not surface area).