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Surface Area Calculator

Calculate the surface area and volume of spheres, cylinders, cones, cubes, and rectangular prisms.

What is Surface Area Calculator?

The surface area calculator computes the total surface area and volume for five common 3D shapes: sphere, cylinder, cone, cube, and rectangular prism. Select a shape, enter the required dimensions, and get both measurements instantly.

How to use

  1. 1 Select the 3D shape from the dropdown menu.
  2. 2 Enter the required dimensions (radius, height, side lengths).
  3. 3 Click Calculate to see surface area and volume.
  4. 4 Switch shapes to calculate different geometries.
  5. 5 All inputs accept decimal values.

Formula

Sphere: SA = 4πr², V = (4/3)πr³. Cylinder: SA = 2πr² + 2πrh, V = πr²h. Cone: SA = πr² + πrl (l=√(r²+h²)), V = (1/3)πr²h. Cube: SA = 6a², V = a³. Rect. prism: SA = 2(lw+lh+wh), V = lwh.

Example calculation

Cylinder with r=3, h=10: SA = 2π(9) + 2π(3)(10) = 18π + 60π = 78π ≈ 245.04. V = π(9)(10) = 90π ≈ 282.74.

Frequently asked questions

What is the difference between surface area and volume?

Surface area is the total area of all outer faces of a 3D object (measured in square units). Volume is the amount of space the object occupies (measured in cubic units).

What is the slant height of a cone?

The slant height l is the distance from the apex to the edge of the base along the side: l = √(r² + h²). It differs from the vertical height h.

Can I use this for real-world applications?

Yes. Surface area calculations are used for painting, wrapping, coating, and material estimation. Volume calculations help with capacity, weight, and fluid problems.

What units should I use?

Use consistent units for all dimensions. The surface area will be in the square of your input unit, and volume in the cube.

How is a rectangular prism different from a cube?

A cube has all equal sides (a × a × a). A rectangular prism (cuboid) can have three different side lengths (l × w × h).