How to Use
Choose the 3D shape from the dropdown — Cube, Cuboid, Cylinder, Cone, Sphere, or Hemisphere.
Fill in the required measurements (radius, height, side, etc.) in any unit — results will be in the same unit.
See Volume, Curved Surface Area, and Total Surface Area instantly with complete step-by-step formula working.
Volume & Surface Area Formulas
| Shape | Volume | Curved SA | Total SA |
|---|---|---|---|
| Cube (side a) | a³ | 4a² | 6a² |
| Cuboid (l, w, h) | l×w×h | 2h(l+w) | 2(lw+wh+lh) |
| Cylinder (r, h) | πr²h | 2πrh | 2πr(r+h) |
| Cone (r, h) | ⅓πr²h | πrl | πr(r+l) |
| Sphere (r) | ⁴⁄₃πr³ | 4πr² | |
| Hemisphere (r) | ⅔πr³ | 2πr² | 3πr² |
* Slant height of cone: l = √(r² + h²) | π = 3.14159… (22/7 for exam problems)
Frequently Asked Questions
Volume = πr²h. Curved Surface Area = 2πrh. Total Surface Area = 2πr(r + h). For r = 7, h = 10 using π = 22/7: Volume = 1540, CSA = 440, TSA = 748.
Volume = (1/3)πr²h. Slant height l = √(r² + h²). CSA = πrl. TSA = πr(r + l). A cone's volume is exactly one-third of a cylinder with the same radius and height.
Curved (Lateral) Surface Area covers only the side surface, excluding bases. Total Surface Area includes all faces. For a cylinder: CSA = 2πrh (sides only); TSA = 2πrh + 2πr² = 2πr(r + h).
A hemisphere is exactly half a sphere. Volume = (2/3)πr³. CSA = 2πr² (curved part only). TSA = 3πr² (curved + flat circular base). The flat base adds one extra πr² compared to CSA.
Volume and Surface Area (Mensuration 3D) questions appear in SSC CGL, CHSL, IBPS PO, Railway, and CAT. Common types: cost of painting/filling a tank, melting one solid into another, comparing volumes, and finding dimensions from given volume or surface area.