Surface Areas and Volumes

Board: GSEB Class: 10

Chapter Overview

Formulas for surface area and volume of common solids: cube (side a), cuboid (l x b x h), right circular cylinder, right circular cone, sphere, hemisphere, and frustum of a cone. Problems involve finding surface areas and volumes of combinations of solids, conversion from one shape to another, and determining the number of smaller solids from a larger one. The volume of a frustum of a cone is (1/3)pi h(R² + r² + Rr), and its curved surface area is pi l(R + r), where l is the slant height.

Topics Covered

Cube and Cuboid
Cylinder
Cone
Sphere
Hemisphere
Frustum of Cone
Combined Solids
Shape Conversion
Volume and Capacity

Key Formulas

Cube: V = a³, SA = 6a²

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

Frustum: V = (1/3)pi h(R²+r²+Rr), CSA = pi l(R+r)

Real-World Applications

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

Study Tips

Tip: Learn all volume formulas systematically

Tip: Practice combination solid problems

Tip: Understand the frustum derivation