Cone Area Calculator

Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature. A figure having an area is called quadratic. Find the area of more than 22 shapes (triangle, square, pentagon, etc.) using our amazing calculator.

Cone — is a body in Euclidean space obtained by combining all the rays emanating from one point (vertex of the cone) and passing through a flat surface. Sometimes a cone is a part of such a body that has a limited volume and is obtained by combining all the segments connecting the vertex and the points of a flat surface (in this case latter is called the base of the cone, and the cone is called leaning on this base). If the base of the cone is a polygon, such a cone is a pyramid.

Calculating the area of a cone is an important skill in geometry and engineering. Our cone lateral and total surface area calculator makes it easy to find the area of your cone based on your inputs.

Formula for Cone Area

The area of the cone is calculated by summing the area values of the circle lying at the base and area of the side surface of the figure. The initial data for its calculation is the radius R and the generator l. The formula for finding the area of a cone is:

S = \pi r^2 + \pi rl

where S is the area, r is the radius of the circular base, l is the slant height, and π is the mathematical constant pi (approximately equal to 3.14).

The first part of the formula, πr², gives the area of the circular base of the cone. The second part of the formula, πrl, gives the area of the curved surface of the cone.

Formula for Cone Lateral Surface Area

The lateral surface area of a cone refers to the area of the curved surface that connects the base of the cone to its apex. The formula for the lateral surface area of a cone is:

L = \pi rl

where L is the lateral surface area, r is the radius of the circular base, l is the slant height, and π is the mathematical constant pi (approximately equal to 3.14).

How to Use the Cone Area Calculator

To use our cone area calculator:

1. Select the type of surface area you want to calculate (lateral or total surface area).
2. Enter the radius of the circular base (r) of your cone in the first box.
3. Enter the slant height (l) of your cone in the second box.
4. Our calculator will automatically calculate the area of your cone.

Example

Let's say we have a cone with a circular base of radius 3 cm and a slant height of 5 cm. Using the formulas above, we can calculate the area, lateral surface area, and total surface area of the cone.

• The lateral surface area of the cone is: S = 3*5 \pi = 47.12 cm^2
• The total surface area of the cone is: S = 3\pi(3+5) = 75.4 cm^2

Using our cone area and surface area calculator, we can verify these results by entering 3 cm as the radius and 5 cm as the slant height. The calculator will automatically calculate the lateral surface area, and total surface area of the cone as 47.12 cm², and 75.4 cm², respectively.

Whether you are a student learning about cones in geometry class or an engineer designing a cone-shaped structure, our cone area and surface area calculator is a useful tool for quickly finding the area and surface area of a cone.