worldofcalcsVolume and Surface Area Calculator
Volume
1,540 cm³
Curved / lateral surface area
440 cm²
Total surface area
748 cm²
Capacity: 1.54 litres
Working
V = πr²h = 22/7 × 7² × 10 = 1,540
CSA = 2πrh = 2 × 22/7 × 7 × 10 = 440
TSA = 2πr(r + h) = 2 × 22/7 × 7 × (7 + 10) = 748
What are volume and surface area?
Volume is the space inside a solid, in cubic units such as cm³. Surface area is the total area of its outside faces, in square units. The curved (or lateral) surface area leaves out the top and bottom; the total surface area includes them. This calculator gives all three for the solids in the NCERT surface areas and volumes chapter, with the capacity in litres.
Volume and surface area formulas
Cylinder: V = πr²h, CSA = 2πrh · Cone: V = ⅓πr²h, CSA = πrl, l = √(r² + h²) · Sphere: V = ⁴⁄₃πr³, SA = 4πr² · Cuboid: V = lbh, TSA = 2(lb + bh + hl)
r is the radius, h the height and l the slant height of a cone. 1,000 cm³ is 1 litre, and 1 m³ is 1,000 litres.
Good to know
- A cone has exactly one third the volume of a cylinder with the same radius and height.
- A hemisphere's total surface area (3πr²) includes its flat circular base; its curved surface is 2πr².
- To find how much paint a tank needs, use the surface area; to find how much water it holds, use the volume.
- Doubling every dimension multiplies the surface area by 4 and the volume by 8.
- 1 m³ = 1,000 litres, and 1 cubic foot is about 28.3 litres.
Worked example: a cone of radius 7 cm and height 24 cm
- Slant height l = √(7² + 24²) = √625 = 25 cm
- Volume = ⅓ × 22/7 × 7² × 24 = 1,232 cm³ (1.232 litres)
- Curved surface area = πrl = 22/7 × 7 × 25 = 550 cm²
- Total surface area = πr(l + r) = 22/7 × 7 × 32 = 704 cm²
Volume and surface area formulas
The formulas for each solid.
| Solid | Volume | Curved / lateral surface | Total surface |
|---|---|---|---|
| Cube | a³ | 4a² | 6a² |
| Cuboid | l × b × h | 2h(l + b) | 2(lb + bh + hl) |
| Cylinder | πr²h | 2πrh | 2πr(r + h) |
| Cone | ⅓πr²h | πrl | πr(l + r) |
| Sphere | ⁴⁄₃πr³ | 4πr² | 4πr² |
| Hemisphere | ⅔πr³ | 2πr² | 3πr² |
For a sphere the curved surface is the whole surface.