Class 10 Maths Chapter 12 (formerly Chapter 13), Surface Areas and Volumes, moves from single basic solids (cuboid, cube, cylinder, cone, sphere and hemisphere) to combinations of solids found in everyday objects—capsules, tents, toys, vessels, silos and गुलाब जामुन (gulab jamuns).
What Class 10 Mathematics (Ganit — Hindi Medium) Chapter 12 Covers
12.1 Surface Area of a Combination of Solids shows that the total surface area of a combined solid equals the sum of the visible curved/flat outer surfaces of its constituent parts (excluding the joined circular base where two solids meet)—for example, a cylinder capped by two hemispheres (2π rh + 2 × 2π r2) or a cone mounted on a hemisphere (π rl + 2π r2, where l = √(r2 + h2)).
12.2 Volume of a Combination of Solids shows that the volume of a solid formed by joining two basic solids is the sum of the volumes of its constituent parts (or the difference when a cavity is hollowed out), using cylinder volume π r2h, cone volume 1/3π r2h, sphere volume 4/3π r3 and hemisphere volume 2/3π r3.
Exercises in Chapter 12
- Exercise 12.1 (9 Questions) calculates surface areas of two cubes joined end-to-end, a hollow hemisphere mounted by a cylinder, a toy cone on a hemisphere, a hemisphere surmounted on or scooped out of a cubical block, a medicine capsule, a cylindrical tent with a conical top, and a cylinder with two hemispherical ends scooped out.
- Exercise 12.2 (8 Questions) computes volumes of a cone on a hemisphere, Rachel’s cylinder-plus-two-cones engineering model, sugar syrup in 45 gulab jamuns, a pen stand with four conical depressions, lead shots dropped into a full inverted cone, a two-cylinder iron pole, a right circular cone + hemisphere placed inside a cylinder full of water, and a spherical glass vessel with a cylindrical neck.
Read Class 10 Mathematics (Ganit — Hindi Medium) Chapter 12 Online
More Chapters
- Previous: Chapter 11: वृत्तों से संबंधित क्षेत्रफल (Areas Related to Circles)
- Next: Chapter 13: सांख्यिकी (Statistics)
- English medium: Class 10 Maths Chapter 12 PDF in English
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FAQ
Why can’t we simply add the total surface areas of two solids when they are joined together?
When two solids are joined together (for example, a cone mounted on a hemisphere of the same radius), the circular flat bases where they meet are hidden inside the combined solid and are no longer part of the outer surface. Only the visible curved surface areas (π rl + 2π r2) form the new total surface area.
What are the volume formulas for a cylinder, cone, sphere and hemisphere of radius r?
Cylinder: π r2h; Cone: 1/3π r2h; Sphere: 4/3π r3; Hemisphere: 2/3π r3.