With Omni's lateral area of a cone calculator, you'll be able to determine the lateral area of a right cone in a blink of an eye!

Maybe you're wondering how to find the lateral area of a cone and even wondering if there's any difference between its surface area and lateral area, well, you just arrived at the right place!

If you like to learn about these and more, we invite you to keep reading and find:

  • The lateral area formula of a cone;
  • What is the difference between lateral area and surface area;
  • How to find the lateral area of a cone using its diameter; and
  • Is it true that the lateral of a cone is exactly 1/2 of the lateral surface area of a cylinder? 🤔

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

The lateral surface area of a cone is given by the expression:

A_L = π x r x √(r² + h²)

Or, in terms of the cone's slant:

A_L = π x r x l

Where:

  • A_L - Lateral surface area;
  • r - Radius of the circular base of the cone;
  • h - Vertical height of the cone; and
  • l - Slant height.

What is the difference between lateral area and surface area?

From the equation above, you might have noticed that the lateral surface area of a cone does not correspond to its total surface area, given by:

A_T = π x r x √(r² + h²) + π x r²

For any geometrical figure, the difference between these two areas is that the lateral surface area of a three-dimensional shape is the area that can be seen from a side-on view. This is, the sides of the shape, excluding its base and top. For the particular case of a cone, we'll only be excluding the base since this figure does not have a top.

The latter equation shows that the total surface area includes the lateral area π x r x √(r² + h²) and the area of the cone's circular base π x r²:

A_T = Total area = Lateral area + base area
A_T = π x r x (√(r² + h²) + r)

From here we can see that if the total and base areas of a cone are known, we could also determine its lateral surface area as the difference between these:

A_L = Lateral area = Total area - base area

Another option to calculate the lateral area of a cone is from its volume and radius or volume and vertical height. This means that if you know any of these, the lateral area of a cone calculator will be able to determine the lateral area of the cone 😉

How do I find the lateral area of a cone?

To find the lateral area of a cone:

  1. Use the cone's lateral area formula, A_L = π x r x √(r² + h²).
  2. To employ this formula, you'll need to know the cone's radius and vertical height.
  3. With these two knowns, you can proceed to substitute the values and perform the required algebraic operation.

For example, if we had a cone of radius r = 6 cm and height h = 10 cm, we can determine its lateral area by:

  1. Using the formula A_L = π x r x √(r² + h²).
  2. Substitute the corresponding dimensions: A_L = 3.1416 x (6 cm) x √((6 cm)² + (10 cm)²).
  3. Finally, execute the required operations, and get the result: A_L = 219.8 cm².

More right circular cone calculators!

If you enjoyed the lateral area of a cone calculator, and want to learn more about right cone's geometrical properties, we invite you to visit other of our related tools:

FAQ

Is the lateral surface area of a cone exactly 1/2 the lateral area of a cylinder?

True. For a cone of slant "h" and a cylinder of height "h", both with the same radius "r", the lateral area of the cone is 1/2 the lateral area of the cylinder:

  1. The formulas for the lateral areas: A_L_cone = π x r x h and A_L_cylinder = 2 x π x r x h.
  2. From these, 2 x A_L_cone = A_L_cylinder.
  3. Thus, A_L_cone = A_L_cylinder/2. Indicating that a cone's lateral area is 1/2 of the cylinder's.

How do I find the lateral area of a cone given its diameter?

To find the lateral of a cone given its diameter D, follow these steps:

  1. Use the lateral area formula for a cone: A_L = π x r x √(r² + h²).
  2. Since the diameter D is equal to twice the radius of a circumference, employ the corresponding relationship: r = D / 2.
  3. By replacing this in the equation above: A_L = π x (D / 2) x √((D / 2)² + h²).
  4. Substitute the numeric values of diameter and height, perform the operations, and get the lateral area value.
Gabriela Diaz
Diagram of a right circular cone.
Radius (r)
in
Height (h)
in
Slant height (l)
in
Results
Lateral surface area (A_L)
in²
Surface area (A)
in²
Base area (A_B)
in²
Volume (V)
cu in
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