Cone Calculator

Instructions:

• Enter the radius and height for the cone.
• Choose the units (cm, m, km, mile, yard, inch) for both radius and height.
• Click "Calculate" to calculate the volume and surface area of the cone.
• Your calculation history will be displayed below.
• Click "Clear" to clear the inputs and results.
• Click "Copy Result" to copy the calculation result to the clipboard.

Enter the Radius: cm m km mile yard inch

Enter the Height: cm m km mile yard inch

Calculate Clear Copy Result

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Calculation Details:

Calculation History:

The Cone Calculator is a tool that helps you calculate the various properties of a right circular cone, given any two known variables. It is a simple and easy-to-use tool that can be used by anyone who has basic knowledge of geometry.

Concepts

The concept of calculating the properties of a cone is based on the idea of finding the volume, surface area, slant height, and other properties of a cone. The calculator does this for us automatically.

Formulae

The formulae used by the calculator to calculate the properties of a cone are as follows:

Volume

V = (1/3)πr^2h

where V is the volume of the cone, r is the radius of the base of the cone, and h is the height of the cone.

Surface Area

A = πr(r + l)

where A is the surface area of the cone, r is the radius of the base of the cone, and l is the slant height of the cone.

Slant Height

l = √(r^2 + h^2)

where l is the slant height of the cone, r is the radius of the base of the cone, and h is the height of the cone.

Benefits

The Cone Calculator has several benefits, including:

Accuracy

The calculator is very accurate and can calculate the properties of a cone with a high degree of precision. It eliminates the possibility of human error in calculations.

Speed

The calculator is fast and can calculate the properties of a cone in a matter of seconds. This saves time and effort, especially when dealing with large cones.

Understanding

The calculator helps users understand the concept of calculating the properties of a cone. It shows the steps involved in finding the volume, surface area, slant height, and other properties of a cone.

Real-life Applications

The concept of calculating the properties of a cone is used in many real-life situations, such as architecture, engineering, and construction. The calculator helps users apply this concept in practical situations.

Interesting Facts

Here are some interesting facts about cones:

• A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex.
• The volume of a cone is exactly one-third the volume of a cylinder with the same base and height.
• The ancient Egyptians and Greeks used cones in their architecture and art.
• The cone is one of the oldest and most basic geometric shapes, and mathematicians have studied it for thousands of years.

References

Here are some scholarly references that you may find useful:

• Weisstein, E. W. (2022). Cone. Wolfram MathWorld¹
• O’Connor, J. J., & Robertson, E. F. (2000). Cone. School of Mathematics and Statistics, University of St Andrews²
• Coxeter, H. S. M. (1969). Introduction to Geometry (2nd ed.). Wiley³

Last Updated : 25 November, 2023