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Volume and Surface Area
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.
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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
A cuboid is the simplest prism: V = l × b × h and SA = 2(lb + bh + hl). Surface area means adding up the area of every flat face.
A cone holds exactly one-third of the cylinder on the same base and height. Unroll a cylinder's curved side and you get a rectangle 2 pi r wide and h tall - that is why curved SA = 2 pi r h.
The radius, vertical height and slant height of a cone form a right-angled triangle, so Pythagoras gives l. Curved surface area uses the slant height l, never the vertical height h.
A toy of a cone on a hemisphere = volume of cone + volume of hemisphere. For surface area, count only the surfaces you can actually see - the joined faces are hidden.
Hard words & meanings
| volume | the amount of three-dimensional space a solid occupies, measured in cubic units |
| surface area | the total area of all the outer faces of a solid, measured in square units |
| prism | a solid with the same cross-section all along its length |
| cross-section | the flat shape you get when you slice straight through a solid |
| slant height | the distance from the apex of a cone to the edge of its base, l = sqrt(r² + h²) |
| hemisphere | exactly half a sphere, with one flat circular face |
| apex | the single pointed top vertex of a cone or pyramid |
| composite solid | a shape made by joining two or more basic solids together |
Model exam answers, grammar & audio
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