NCERT Solutions Class 10 Maths Chapter 12 — Surface Areas and Volumes#
Chapter 12 extends earlier knowledge of mensuration to solid figures formed by combining basic shapes such as cones, cylinders, spheres, and hemispheres. You will find the surface area and volume of these combined solids and solve problems involving the conversion of one solid into another.
Exercises#
- Exercise 12.1 — Surface area of combinations of solids (9 questions)
- Exercise 12.2 — Volume of combinations of solids and conversion of solids (8 questions)
What you will learn#
- Surface areas of solids made by combining cubes, cuboids, cylinders, cones, spheres and hemispheres.
- Volumes of such combined solids.
- Real objects: tents, toys, capsules, vessels and pen stands.
Key formulas and results#
- Cylinder: curved surface area $2\pi rh$, volume $\pi r^2 h$.
- Cone: curved surface area $\pi rl$, volume $\dfrac{1}{3}\pi r^2 h$.
- Sphere: surface area $4\pi r^2$, volume $\dfrac{4}{3}\pi r^3$. Hemisphere: curved surface area $2\pi r^2$, volume $\dfrac{2}{3}\pi r^3$.
Read and revise#
- Class 10 Maths Notes — Surface Areas and Volumes: every definition, formula and method in short.
- All Class 10 Maths formulas on one page.
- NCERT Class 10 Maths Chapter 12 (PDF) — the textbook chapter itself, and all Class 10 Maths chapters.
Frequently asked questions#
How many exercises are in Class 10 Maths Chapter 12?
Two: Exercise 12.1 (9 questions) and Exercise 12.2 (8 questions) — 17 questions in all, each solved step by step here.
What do you leave out when finding the surface area of a combined solid?
The faces where the solids are joined, because they are hidden inside. Add only the surfaces that stay on the outside. For volume, simply add the volumes of the parts.