Cone Surface Area Calculator
Effortlessly calculate the surface area of a cone. Understand base, lateral, and total areas with visual clarity.
Enter Cone Dimensions
Provide radius and height to calculate surface areas.
units
units
Surface Area Results
Base Surface Area ( \( \pi r^2 \) ):
Lateral Surface Area ( \( \pi rl \) ):
Total Surface Area:
Understanding Cone Surface Area
A cone is a 3D shape with a circular base and a vertex. Calculating its surface area involves understanding two main components: the base and the lateral surface.
Formulas Explained
- Base Area: The area of the circular base. Formula: $$ A_{base} = \pi r^2 $$, where \( r \) is the radius.
- Lateral Surface Area: The area of the curved surface. Formula: $$ A_{lateral} = \pi r l $$, where \( l \) is the slant height, calculated as $$ l = \sqrt{r^2 + h^2} $$, with \( h \) being the height of the cone.
- Total Surface Area: Sum of the base and lateral surface areas. Formula: $$ A_{total} = A_{base} + A_{lateral} = \pi r^2 + \pi r l $$
How to Use This Calculator
Simply enter the radius and height of the cone in the input fields. Click 'Calculate' to get the base, lateral, and total surface areas instantly. Use 'Reset' to clear inputs and start again. Copy results for easy sharing or record-keeping.