Cone Surface Area Calculator

Find the slant height, lateral conical area, and total surface area of any right circular cone.

▲ Cone Surface Area Calculator

Formula: A = πr(r + l)

Base Radius (r) *

Cone Height (h) *

Decimal Precision

Calculated Cone Surface Area

91.4984 cm²

Step-by-Step Mathematical Breakdown:

1. Radius \( r = 3\text{ cm} \), Height \( h = 6\text{ cm} \)

2. Slant Height: \( l = \sqrt{r^2 + h^2} = \sqrt{9 + 36} \approx 6.7082\text{ cm} \)

3. Conical Lateral Area: \( \pi r l \approx \pi(3)(6.7082) \approx 63.2241\text{ cm}^2 \)

4. Base Circular Area: \( \pi r^2 = \pi(9) \approx 28.2743\text{ cm}^2 \)

5. Total Area: \( A \approx 63.2241 + 28.2743 \approx \mathbf{91.4984\text{ cm}^2} \)

What is the formula for the surface area of a cone?

Total surface area is A = πrl + πr² = πr(r + l), where r is base radius and l is slant height.

What is slant height l?

Slant height l is the distance from the apex along the curved surface down to the edge of the circular base: l = √(r² + h²).