What's the difference between surface area and volume?

Surface area measures the total area of all outer surfaces (in square units), while volume measures the space inside the object (in cubic units). Think of surface area as the amount of paint needed to cover an object, and volume as how much it can hold.

How do I calculate the slant height of a cone?

Slant height (l) = √(r² + h²) where r is the radius and h is the height. This uses the Pythagorean theorem, treating the radius, height, and slant height as sides of a right triangle.

Why does a sphere have the smallest surface area for its volume?

Among all shapes with the same volume, a sphere has the minimum surface area. This is why bubbles are spherical - they minimize surface tension. This property is important in physics, biology, and engineering.

How is surface area used in real applications?

Surface area calculations are used for determining paint or material quantities, heat transfer calculations, drug dosage based on body surface area, packaging design, and architectural planning.

Surface Area Calculator – 3D Shape Surface Area

Calculate surface area of 3D shapes including spheres, cubes, cylinders, cones, and pyramids. Essential for geometry and real-world applications.

Surface Area Calculator – 3D Shape Surface Area

Calculate surface area of 3D shapes including spheres, cubes, cylinders, cones, and pyramids. Essential for geometry and real-world applications.

Shape*

Select the 3D shape

First Dimension*

Radius, side length, or first measurement

Second Dimension

Height, width, or second measurement

Third Dimension

Depth or third measurement

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Math visualization will appear here

Understanding Surface Area

Surface area measures the total area of all faces of a 3D object. It's important for calculating material needs, heat transfer, painting requirements, and many engineering applications.

Surface Area Formulas

Common surface area formulas:

Sphere: SA = 4πr²
Cube: SA = 6s² (6 times side squared)
Cylinder: SA = 2πr(r + h)
Cone: SA = πr(r + l) where l is slant height
Rectangular Prism: SA = 2(lw + lh + wh)
Square Pyramid: SA = s² + 2s√((s/2)² + h²)

How to Use This Calculator

Follow these simple steps to get accurate results:

Enter your shape
Enter your first dimension
Enter your second dimension
Enter your third dimension
Click the "Calculate" button to see your results
Review the detailed breakdown and explanation

Why Use Our Surface Area Calculator – 3D Shape Surface Area?

100% free and no registration required
Instant, accurate calculations with professional formulas
Mobile-friendly design that works on any device
Privacy-focused - your data never leaves your browser
Educational content to help you understand the results

Frequently Asked Questions

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