NCERT Solutions for Class 10 Maths Chapter 12 Surface Areas and Volumes
NCERT Solutions for Class 10 Maths Chapter 12 Surface Areas and Volumes covers surface areas and volumes of combinations of solids, conversion of one solid into another, and problems on the frustum of a cone.
Overview of Topics & Subtopics (Click to Jump)
1. Surface Area of a Combination of Solids
Short Note:
• When two or more basic solids (cube, cuboid, cylinder, cone, sphere, hemisphere) are combined, the total surface area of the combination is found by adding the exposed curved/flat surface areas of each part — not simply adding their individual total surface areas.
2. Volume of a Combination of Solids
Short Note:
• The volume of a combined solid is found by adding (or subtracting, for hollowed-out solids) the volumes of the individual basic solids that make up the shape.
3. Conversion of Solid from One Shape to Another
Short Note:
• When a solid is recast/converted into another shape, its volume remains constant; this principle is used to find unknown dimensions after melting and recasting.
4. Frustum of a Cone
Short Note:
• A frustum is the part of a cone that remains after its upper part (with a smaller cone) is cut off by a plane parallel to the base.
• For a frustum with radii r1, r2 and height h, slant height l = √[h²+(r1−r2)²]; Volume = ⅓πh(r1²+r2²+r1r2); Curved Surface Area = π(r1+r2)l.
NCERT Textbook Exercise Questions
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These short notes are designed for quick revision. Read the main points once, then use the related material below to practise the same chapter. Revising a concept and checking it with questions can make your preparation more focused.