Surface Area of a Cone in Square Feet Calculator
Calculate the total and lateral surface area of a cone with our interactive 3D calculator
Calculator
Lateral Surface Area:
0 ft²
Total Surface Area:
0 ft²
Slant Height:
0 ft
Surface Area Formulas
Slant Height (s)
Where r is the radius and h is the height of the cone.
Lateral Surface Area
Where r is the radius and s is the slant height.
Total Surface Area
The sum of the base area (πr²) and the lateral surface area (πrs).
Practical Applications
Construction Industry
Used to calculate the material needed for conical roofs, towers, or silos. Helps estimate painting area, roofing materials, or siding requirements.
Manufacturing
Essential for designing and producing conical components, containers, or hoppers. Helps determine material costs and weight calculations.
Engineering & Design
Used in designing ventilation systems, ductwork, and funnels. Critical for heat transfer calculations and thermal analysis of conical surfaces.
Understanding Surface Area of a Cone
What is a Cone?
A cone is a three-dimensional geometric shape that tapers from a flat, circular base to a point called the apex or vertex. It is formed by a set of line segments connecting the apex to all points on the base.
Surface Area Components
The surface area of a cone consists of two parts:
- Base Area: The circular base with area πr²
- Lateral Surface Area: The curved surface with area πrs
Slant Height
The slant height is the straight-line distance from the apex to the edge of the base. It forms the hypotenuse of a right triangle with the height and radius.
Step-by-step Calculation
- Measure the radius (r) of the circular base in feet
- Measure the height (h) of the cone in feet
- Calculate the slant height: s = √(r² + h²)
- Calculate the lateral surface area: πrs
- Calculate the base area: πr²
- Add the lateral and base areas to find the total surface area: πr² + πrs
Measurement Tips
- Always use consistent units (in this case, feet)
- For irregular cones, calculate an average radius
- When measuring existing structures, measure the slant height directly for more accuracy
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