Surface Areas and Volumes

This chapter measures real solids built from the five basic shapes — cuboid, cube, cylinder, cone, sphere and hemisphere. After recalling every base formula (curved and total surface area, and volume), it shows how to find the surface area of a combination of solids (add only the exposed curved surfaces — joined faces disappear) and the volume of a combination (simply add, or subtract for a cavity). It then covers two high-yield board topics: the conversion of a solid from one shape to another by melting and recasting (volume is conserved) and the frustum of a cone (a bucket/glass shape) with its surface-area and volume formulas. It is a formula-heavy, very high-scoring chapter of the Class 10 Board syllabus.