Surface Area Calculator

How to Calculate Surface Area

Surface area is the total area of the outer surface of a three-dimensional object. The method for calculating surface area depends on the shape of the object. Here are the formulas and steps for common shapes:

Surface Area Formulas

• Cube: \(SA = 6s^2\), where \(s\) is the side length
• Sphere: \(SA = 4\pi r^2\), where \(r\) is the radius
• Cylinder: \(SA = 2\pi r(r + h)\), where \(r\) is the radius of the base and \(h\) is the height
• Cone: \(SA = \pi r(r + \sqrt{r^2 + h^2})\), where \(r\) is the radius of the base and \(h\) is the height

Calculation Steps

1. Identify the shape of the object
2. Measure or note the required dimensions (e.g., side length, radius, height)
3. Choose the appropriate formula for the shape
4. Substitute the measured values into the formula
5. Perform the calculations to find the surface area

Example Calculation

Let's calculate the surface area of a cylinder with radius 5 cm and height 10 cm:

1. Shape: Cylinder
2. Dimensions: \(r = 5\) cm, \(h = 10\) cm
3. Formula: \(SA = 2\pi r(r + h)\)
4. Substitution: \(SA = 2\pi \times 5 \times (5 + 10)\)
5. Calculation: \(SA = 2\pi \times 5 \times 15 = 150\pi \approx 471.24\) cm²

Visual Representation

This diagram illustrates a cylinder with radius 5 cm and height 10 cm. The surface area includes the circular top and bottom bases, as well as the curved lateral surface.