Truncated 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.

A truncated cone is the part of the cone enclosed between the base and the secant plane parallel to the base.

A truncated cone is a three-dimensional object that is formed by cutting the top off a larger cone with a plane parallel to its base. The total surface area of a truncated cone is the sum of the areas of its circular base, its top circular base, and its lateral surface. The lateral surface area of a truncated cone is the area of the curved surface between the top and bottom bases.

Formula for Truncated Cone Area

The formula for the total surface area of a truncated cone is:

S = \pi (r_1^2 + (r_1+r_2)l + r_2^2)

where S is the total surface area, r₁ and r₂ are the radii of the top and bottom circular bases, and l is the slant height of the truncated cone. The formula for the lateral surface area of a truncated cone is:

L = \pi l(r_1+r_2)

where L is the lateral surface area.

How to Use the Truncated Cone Area Calculator

Our truncated cone area calculator makes it easy to find the total surface area and lateral surface area of your truncated cone. To use the calculator:

• Select the type of surface area you want to calculate (lateral or total surface area).
• Enter the radius (r₁) of the bottom circular base in the first box.
• Enter the radius (r₂) of the top circular base in the second box.
• Enter the height (l) of the truncated cone in the third box.
• Calculator will automatically calculate the area of your truncated cone.

Example of Truncated Cone Area Calculation

For example, let's say we have a truncated cone with a bottom circular base radius of 5 cm, a top circular base radius of 3 cm, and a height of 10 cm. The total surface area of the truncated cone can be calculated as follows:

S = \pi (5^2 + 8*10 + 3^2 ) = 358.14 cm^2

The lateral surface area of the truncated cone can be calculated as:

S = 10\pi (5+3) = 251.3 cm^2

Conclusion

Calculating the total surface area and lateral surface area of a truncated cone can be challenging, but our truncated cone area calculator and formula make it easy. Try it out for yourself and see how easy it can be to calculate the area of your truncated cone!