Surface areas and volumes · पृष्ठीय क्षेत्रफल और आयतन
Cylinder, cone, sphere and hemisphere — pick the right formula, then work it out.
Surface areas and volumes games
Formulas पृष्ठीय क्षेत्रफल और आयतन
| Solid | Curved / lateral surface area | Total surface area | Volume |
|---|---|---|---|
| Cuboid | 2h(l + b) | 2(lb + bh + hl) | lbh |
| Cube | 4a² | 6a² | a³ |
| Cylinder | 2πrh | 2πr(r + h) | πr²h |
| Cone | πrl, l = √(r² + h²) | πr(l + r) | ⅓πr²h |
| Sphere | 4πr² | 4πr² | 4/3 πr³ |
| Hemisphere | 2πr² | 3πr² | 2/3 πr³ |
Tip: take π = 22/7 when the radius is a multiple of 7 — the 7s cancel. Areas are in cm², volumes in cm³; 1 litre = 1000 cm³.
Combined solids (Class 10): add the volumes; for the surface area add only the parts you can touch from outside. Example: a toy made of a cone on a hemisphere. Also see the mensuration formulas chart and faces, edges and vertices.
Goes with NCERT Mathematics Class 9 (Surface Areas and Volumes) and Class 10 (Surface Areas and Volumes). Answers worked out exactly with π = 22/7.
A one-page chart to stick on the wall, and a worksheet to practise.
Surface areas and volumes
Formulas पृष्ठीय क्षेत्रफल और आयतन
| Solid | Curved / lateral surface area | Total surface area | Volume |
|---|---|---|---|
| Cuboid | 2h(l + b) | 2(lb + bh + hl) | lbh |
| Cube | 4a² | 6a² | a³ |
| Cylinder | 2πrh | 2πr(r + h) | πr²h |
| Cone | πrl, l = √(r² + h²) | πr(l + r) | ⅓πr²h |
| Sphere | 4πr² | 4πr² | 4/3 πr³ |
| Hemisphere | 2πr² | 3πr² | 2/3 πr³ |
Tip: take π = 22/7 when the radius is a multiple of 7 — the 7s cancel. Areas are in cm², volumes in cm³; 1 litre = 1000 cm³.
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Surface areas and volumes — worksheet
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