Surface areas and volumes of solids made by combining cubes, cuboids, cylinders, cones, spheres and hemispheres. Our own step-by-step solutions to Exercises 12.1 and 12.2, one page per exercise, set out for step marks.
Each exercise has its own page with every question solved step by step. Pick the one you are on.
What it tests. Add the areas of the faces you can see and leave out any face that is hidden where two solids join. A hemisphere's curved surface is \(2\pi r^2\); a cone's curved surface is \(\pi r l\) with \(l = \sqrt{r^2 + h^2}\); a cylinder's is \(2\pi r h\). Unless the question gives another value, take \(\pi = \tfrac{22}{7}\), as the NCERT exercises do (no calculator: CBSE is a no-calculator exam).
What it tests. Volumes add (or subtract, for a hollow): cylinder \(\pi r^2 h\), cone \(\tfrac13\pi r^2 h\), sphere \(\tfrac43\pi r^3\), hemisphere \(\tfrac23\pi r^3\). Keep units consistent. Unless the question gives another value, take \(\pi = \tfrac{22}{7}\), as the NCERT exercises do (no calculator: CBSE is a no-calculator exam).
Surface Areas and Volumes has 37 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
Also useful: free MCQs and case studies for Surface Areas and Volumes · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan
Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.