13
CBSE Marks
★★★★★
Difficulty
8
Topics
Very High
Board Weight
Topics Covered
8 key topics in this chapter
Surface Area of Cuboid & Cube
Surface Area of Right Circular Cylinder
Surface Area of Right Circular Cone
Surface Area of Sphere & Hemisphere
Volume of Cuboid & Cube
Volume of Cylinder
Volume of Cone
Volume of Sphere & Hemisphere
Study Resources
Key Formulas & Identities
| Formula / Rule | Expression |
|---|---|
| Cuboid TSA | \(2(lb + bh + hl)\) |
| Cube TSA | \(6a²\) |
| Cylinder CSA | \(2πrh\) |
| Cylinder TSA | \(2πr(r+h)\) |
| Cone CSA | \(πrl (l = slant height = √(r²+h²))\) |
| Cone TSA | \(πr(r+l)\) |
| Sphere SA | \(4πr²\) |
| Hemisphere TSA | \(3πr²\) |
| Cuboid Volume | \(l × b × h\) |
| Cube Volume | \(a³\) |
| Cylinder Volume | \(πr²h\) |
| Cone Volume | \(⅓πr²h\) |
| Sphere Volume | \(⁴⁄₃πr³\) |
| Hemisphere Volume | \(⅔πr³\) |
Important Points to Remember
Lateral (Curved) Surface Area excludes the base(s). Total Surface Area includes all faces. Always read the problem carefully.
Slant height of a cone: l = √(r² + h²). This follows from Pythagoras — the slant is the hypotenuse.
A hemisphere has curved SA = 2πr² and flat circular face area = πr², so TSA = 3πr².
Volume formulae to memorise: Cube = a³; Cuboid = lbh; Cylinder = πr²h; Cone = ⅓πr²h; Sphere = ⁴⁄₃πr³; Hemisphere = ⅔πr³.