Case 1
- Base radius
- 3
- Slant height
- 5
75.398224
Open with these valuesCone Surface Area Calculator
75.398224units²
Result: 75.398224 units²This needs the slant height — the diagonal from the rim to the tip — not the vertical height. If you only have the vertical height h, the slant is √(r² + h²). The result is the curved side plus the circular base; leave the base out and you get πrl alone.
The numbers at a glance
Held fixed: Base radius 3.000.
| Slant height | Result |
|---|---|
| 2.000 | 47.123890 |
| 4.000 | 65.973446 |
| 5.000Your value | 75.398224 |
| 6.000 | 84.823002 |
| 8.000 | 103.672558 |
| 10.000 | 122.522113 |
Worked examples
Case 2
- Base radius
- 1
- Slant height
- 1
6.283185
Open with these valuesCase 3
- Base radius
- 5
- Slant height
- 12
267.035376
Open with these valuesHow it's calculated
A = π × r × (r + l)
- StepMeasure the radius of the circular base.
- StepMeasure the slant height along the side, from rim to tip.
- ResultRead the total area in the square of the unit you entered.
Reference table
| Radius, slant | Exact | Total area |
|---|---|---|
| 0.5, 2 | 1.25π | 3.926991 |
| 1, 1 | 2π | 6.283185 |
| 2, 3 | 10π | 31.415927 |
| 3, 5 | 24π | 75.398224 |
| 5, 12 | 85π | 267.035376 |
Questions
How do you find the surface area of a cone?
π times the radius times the sum of the radius and the slant height. A cone with radius 3 and slant 5 has 24π, about 75.4 square units.
What is the slant height?
The straight distance along the side from the edge of the base to the tip. It is always longer than the vertical height, and the two are linked by l = √(r² + h²).
Does this include the base?
Yes. The πr² base circle is the first term; the curved side alone is πrl, which is what you want for a cone with an open bottom, like a party hat.
I only know the vertical height — what now?
Convert it first: square the radius, square the height, add them and take the square root. Radius 3 with height 4 gives a slant of exactly 5.
Sources and last check
Information, not professional advice.