Cone Calculator
Enter radius and height to calculate volume, surface area, and slant height.
Cone Calculator – Find Slant Height, Volume, and Surface Area
A Cone Calculator helps you solve cone measurements when you know the radius and height. By entering these two values, the calculator determines the slant height, volume, and surface area of a cone using standard geometric formulas.
This type of calculator is useful for students, teachers, engineers, architects, and anyone working with three-dimensional shapes in mathematics or real-world applications.
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What Is a Cone?
A cone is a three-dimensional geometric shape with a circular base that narrows smoothly to a single point called the vertex. Common examples include ice cream cones, funnels, party hats, and traffic cones.
To calculate the properties of a cone, two measurements are essential:
- Radius (r) of the circular base
- Height (h) from the center of the base to the vertex
How the Cone Calculator Works
The Cone Calculator uses the radius and height to compute:
- Slant Height
- Volume
- Total Surface Area
Once the values are entered, the calculator applies mathematical formulas to produce accurate results.
Slant Height of a Cone
The slant height is the distance from the edge of the base to the vertex along the curved surface.
Slant Height Formula
Slant Height (l) = √(r² + h²)
Where:
- r = radius
- h = height
The slant height is needed when calculating the surface area of a cone.
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Volume of a Cone
The volume represents the amount of space inside the cone.
Volume Formula
Volume (V) = (1/3) × π × r² × h
Where:
- π ≈ 3.14159
- r = radius
- h = height
Volume is commonly measured in cubic units such as cm³, m³, or in³.
Surface Area of a Cone
The total surface area includes both the curved surface and the circular base.
Surface Area Formula
Surface Area (A) = πr(r + l)
Where:
- r = radius
- l = slant height
Surface area is measured in square units such as cm² or m².
Example Calculation
If a cone has:
- Radius = 5 cm
- Height = 12 cm
Then:
- Slant Height = √(5² + 12²) = √169 = 13 cm
- Volume = (1/3) × π × 5² × 12 ≈ 314.16 cm³
- Surface Area = π × 5 × (5 + 13) ≈ 282.74 cm²
Why Use a Cone Calculator?
Using a cone calculator helps to:
- Reduce calculation errors
- Save time when solving geometry problems
- Understand relationships between cone dimensions
- Apply formulas correctly in academic and practical work
It is especially useful for exams, homework, construction planning, manufacturing, and design projects.
Who Can Use This Calculator?
- Students learning geometry
- Teachers creating examples and assignments
- Engineers and architects
- Designers working with conical shapes
- Anyone needing fast cone measurements
Final Thoughts
A Cone Calculator simplifies geometric calculations by using the radius and height to instantly determine the slant height, volume, and surface area of a cone. Whether you are studying math or applying geometry in real life, this calculator provides clear and reliable results based on standard formulas.
Using a cone calculator ensures consistency, clarity, and confidence when working with three-dimensional shapes.