Truncated cone volume calculator

From ancient times, people needed to measure the amount of various substances. Bulk substances and liquids could be measured by filling them with vessels of a certain capacity, determining their quantity by volume. The concept of volume in solid geometry is introduced similarly to the concept of area in plane geometry. In plane geometry, we determined the area like this: the area of ​​a polygon is the value of the part of the plane that the polygon occupies. To formulate the concept of volume similarly to this concept. The magnitude of the part of the space occupied by the geometric body is called the volume of this body. Volume is measured in "cubic" units.

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

The volume of the truncated cone(volume of frustum) is equal to one third of the height times the number Pi, as well as the sum of the squares of the radii of the truncated pyramid and the product of the radii. The volume of a truncated cone can be calculated using the following formula:

V = \dfrac{1}{3}\pi h \left( r_1^2 + r_1r_2 + r_2^2 \right )

where V is the volume of the truncated cone, h is the height of the truncated cone, and r₁ and r₂ are the radii of the larger and smaller bases of the truncated cone, respectively.

To make it easy for you to find the volume of your truncated cone, we have created this simple and easy-to-use truncated cone volume calculator. To use the calculator:

1. Enter the height of the truncated cone in the first box.
2. Enter the radius of the larger base of the truncated cone in the second box.
3. Enter the radius of the smaller base of the truncated cone in the third box.
4. Our calculator will automatically make all calculations and give the volume of your truncated cone.

Here's an example:

Example: A truncated cone has a height of 10 cm, a larger base radius of 5 cm, and a smaller base radius of 3 cm. To find its volume, simply enter these values into the calculator and the volume will be automatically calculated for you:

Use this calculator anytime you need to quickly and accurately find the volume of a truncated cone.

Truncated Cone Volume Formula

The formula for the volume of a truncated cone is:

V = \dfrac{1}{3}\pi h \left( r_1^2 + r_1r_2 + r_2^2 \right )

where V is the volume of the truncated cone, h is the height of the truncated cone, and r₁ and r₂ are the radii of the larger and smaller bases of the truncated cone, respectively.

Examples of Truncated Cone Volume Calculation

Here are some examples of finding the volume of a truncated cone using the formula:

Example 1: Find the volume of a truncated cone with a height of 10 cm, a larger base radius of 5 cm, and a smaller base radius of 3 cm.

Solution: Using the formula for the volume of a truncated cone, we have:

V = \dfrac{1}{3}\pi 10 \left( 5^2 + 5*3 + 3^2 \right ) ≈ 157.08 cm³

Therefore if you have a truncated cone with a height of 10 cm, a larger base radius of 5 cm, and a smaller base radius of 3 cm, its volume is approximately 157.08 cm³.

Example 2: Find the volume of a truncated cone with a height of 8 inches, a larger base radius of 4 inches, and a smaller base radius of 2 inches.

Solution: Using the formula for the volume of a truncated cone, we have:

V = \dfrac{1}{3}\pi 8 \left( 4^2 + 4*2 + 2^2 \right ) ≈ 100.53 cm³

Therefore, if you have a truncated cone with a height of 8 inches, a larger base radius of 4 inches, and a smaller base radius of 2 inches, its volume is approximately 100.53 in³.

With the truncated cone volume formula and the truncated cone volume calculator, you can easily find the volume of a truncated cone for any given height and base radii. Whether you're working on a math problem or a real-world application, this tool can save you time and effort. Try it out today!