Chapter 10: Surface Areas and Volumes

Surface Areas and Volumes extends Class 8's cube-and-cuboid formulas to cylinders, cones and spheres — covering curved surface area, total surface area, and volume for each. A cylinder's curved surface area alone is 2πrh, while its total surface area adds the two circular ends: 2πrh+2πr².

Confusing curved surface area with total surface area is the most frequent mistake, closely followed by using a diameter where a formula calls for a radius. This is one of the most formula-heavy chapters in Class 9, and every one of these formulas reappears in Class 10's Mensuration, combined into more complex solids like a cone sitting on a hemisphere.