Q1. Find the volume of a cylinder of radius 7 cm and height 10 cm (π = 22/7).
V = πr²h
V = 22/7 × 7² × 10 = 22/7 × 49 × 10
V = 22 × 70 = 1540 cm³
Surface Areas and Volumes — Class 9
Learn the surface area and volume of every basic solid — and compute them instantly by picking a shape.
Surface areaThe total area of the outer surface of a solid (square units).
VolumeThe space a solid occupies (cubic units).
Curved vs total surface areaCSA excludes the flat base(s); TSA (total) includes them.
Mensuration calculator Interactive
Pick a shape, enter the dimensions and read the total surface area and volume (π ≈ 3.1416).
Total surface area—units²
Volume—units³
Numericals practice Interactive
Volume problems with steps.
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Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Cuboid | TSA = 2(lb+bh+hl), V = lbh |
| Cube | TSA = 6a², V = a³ |
| Cylinder | TSA = 2πr(r+h), V = πr²h |
| Cone | TSA = πr(r+l), V = ⅓πr²h |
| Sphere | SA = 4πr², V = 4/3 πr³ |
Common mistakes & exam wins
- CSA leaves out the base; TSA includes it — read the question carefully.
- Use π = 22/7 when the radius is a multiple of 7.
- Slant height of a cone: l = √(r² + h²).
Frequently asked questions
What is the volume of a cuboid?
V = length × breadth × height (l·b·h).
What is the total surface area of a cylinder?
TSA = 2πr(r + h), where r is the radius and h the height.
What is the difference between CSA and TSA?
CSA (curved surface area) excludes the flat base(s); TSA (total surface area) includes them.