Chapter 13 : Surface Areas and Volumes The chapter transitions from simple shapes (learned in Class IX) to complex, real-world objects. Combination of Solids: Objects formed by joining two or more basic solids (e.g., a capsule is a cylinder with two hemispheres). Surface Area Principle: The total surface area (TSA) of a combined solid is the sum of the curved surface areas (CSA) of its individual parts that are visible. Volume Principle: The volume of a combined solid is simply the sum of the volumes of its constituent parts Essential Formulas :

Chapter 12 : Area Related to Circle This chapter transitions from basic circle properties to calculating the areas of specific portions of a circular region, namely the Sector and the Segment. Key Points (Sector and Segment) Sector: The region enclosed by two radii and their corresponding arc. Minor Sector: The smaller portion (e.g., OAPB). Major Sector: The larger portion (e.g., OAQB). Segment: The region enclosed between a chord and its corresponding arc. Minor Segment: The smaller portion (e.g., APB). Major Segment: The larger portion (e.g., AQB). Core Formulas The chapter utilizes the Unitary Method based on a full circle's angle to derive these essential formulas: Practice Questions With Solution