How do you calculate the surface area of a three-dimensional shape?

Calculating the surface area of a three-dimensional shape involves finding the measure of the sum of the areas of its faces. This is a crucial aspect of 3D geometry and is often used in real-life scenarios where objects have varying shapes and sizes that need to be measured or calculated.

The surface area of a prism or cylinder can be found by summing the areas of its faces. For a rectangular prism, the surface area is calculated by adding the area of all its sides, which is given by:

2(lw + lh + wh)

where l, w, and h represent the length, width, and height of the prism, respectively.

Similarly, the surface area of a sphere can be calculated as:

4πr²

where r is the radius of the sphere. The surface area of a cone can be derived by adding the area of the base and the lateral surface area, which is given by:

πr² + πr√(r² + h²)

where r represents the radius of the base, and h represents the height of the cone.