Q1. Find the total surface area of a cube of side 5 cm.
SA = 6a²
SA = 6 × 5²
SA = 6 × 25 = 150 cm²
Surface Areas and Volumes — Class 10
Every solid has just two things to find: its surface area and its volume. Pick a shape, enter the sizes and get both instantly.
Surface areaThe total area of all the outer faces/curved surfaces of a solid. Measured in square units.
VolumeThe space occupied by a solid. Measured in cubic units.
Combinations of solidsReal objects (an ice-cream cone, a capsule) combine shapes — add the relevant curved surfaces and volumes.
Mensuration calculator Interactive
Pick a 3D shape, enter its dimensions and read off the 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 |
|---|---|
| Cube | SA = 6a², V = a³ |
| Cuboid | SA = 2(lb+bh+hl), V = l·b·h |
| Cylinder | CSA = 2πrh, V = πr²h |
| Cone | CSA = πrl, V = ⅓πr²h |
| Sphere | SA = 4πr², V = 4/3 πr³ |
| Hemisphere | CSA = 2πr², V = 2/3 πr³ |
Common mistakes & exam wins
- Surface area is in square units (cm²); volume is in cubic units (cm³) — never mix them up.
- For a combined solid, add only the surfaces that are actually exposed.
- Slant height of a cone: l = √(r² + h²).
- Use π = 22/7 when the radius is a multiple of 7; otherwise 3.14.
Frequently asked questions
What is the volume of a cylinder?
V = πr²h, where r is the base radius and h the height.
What is the surface area of a sphere?
4πr², and its volume is 4/3 πr³.
What is the slant height of a cone?
l = √(r² + h²), where r is the base radius and h the vertical height.