Surface Areas and Volumes

Board: GSEB Class: 9

Chapter Overview

Formulas for 3D solids: cube (side a), cuboid (l x b x h), right circular cylinder (radius r, height h), right circular cone (radius r, height h, slant height l), sphere (radius r), hemisphere (radius r). Surface area can be total (including all faces) or curved/lateral (excluding bases). Problems include finding the cost of painting/covering, capacity of containers, and comparisons between solids.

Topics Covered

Cube and Cuboid
Right Circular Cylinder
Right Circular Cone
Sphere
Hemisphere
Lateral and Total Surface Area
Volume
Capacity Problems

Key Formulas

Cube: V = a³, TSA = 6a²

Cuboid: V = lbh, TSA = 2(lb+bh+lh)

Cylinder: V = pi r² h, CSA = 2pi rh

Cone: V = (1/3)pi r² h, CSA = pi rl

Sphere: V = (4/3)pi r³, SA = 4pi r²

Hemisphere: V = (2/3)pi r³, CSA = 2pi r²

Real-World Applications

Applications: Packaging, tank design, construction, manufacturing, architecture, industrial engineering.

Study Tips

Tip: Learn each formula systematically by shape

Tip: Practice volume conversion problems

Tip: Understand CSA vs TSA for different shapes