Cone Calculator: Slant Height, Volume and Surface Area
Enter the radius and either the vertical height or the slant height. The calculator finds the other one and then the volume and surface areas.
- Nothing you type is stored
- Free
- No signup
Volume
1,231.5043cm³
- Slant height (l)
- 25 cm
- Curved surface area (CSA)
- 549.7787 cm²
- Total surface area (TSA)
- 703.7168 cm²
- Apex angle
- 32.52 °
Show working
- l = √(r² + h²) = √(7² + 24²) = 25 cm
- V = ⅓πr²h = ⅓ × π × 7² × 24 = 1,231.5043 cm³
- CSA = πrl = π × 7 × 25 = 549.7787 cm²
- TSA = πr(l + r) = 703.7168 cm²
How to use
- Choose whether you know the height or the slant height.
- Enter the radius and that value, and pick a unit.
- Read the volume, slant height, CSA and TSA.
Good to know
Slant height l = √(r² + h²), volume = ⅓πr²h, curved surface area = πrl and total surface area = πr(l + r). These are NCERT Class 9 and 10 formulas.
Questions often give the slant height instead of the height: then h = √(l² − r²). For r = 7 and l = 25, h = 24 and the volume is 1,232 cm³ with π = 22/7.
Real uses: cloth for a conical tent (its CSA), the volume of a heap of grain or sand, an ice-cream cone or a funnel. The apex angle is the full angle at the tip.
Questions
What is the slant height of a cone?
The distance from the tip to the edge of the base along the side: l = √(r² + h²).
What is the volume of a cone?
⅓πr²h, one third of a cylinder with the same base and height.
How much canvas does a conical tent need?
Its curved surface area, πrl. Add some extra for stitching and wastage.
What is the TSA of a cone?
πr(l + r): the curved part plus the circular base.
Is anything I enter stored?
No. The calculation runs in your browser and nothing is sent to a server.