To find the surface area of composite 3-D figures, follow these steps:
1. Break down the composite figure into its simple component shapes: Composite 3-D figures can usually be broken down into basic shapes like cubes, cylinders, cones, pyramids, prisms, or spheres. Identify each of the component shapes that make up the composite figure.
2. Determine the surface area formula for each component shape: Look up the surface area formula for each of the component shapes. These formulas are usually available in geometry textbooks or online resources.
3. Calculate the surface area for each component shape: Plug the dimensions of each component shape (such as length, width, height, radius, etc.) into their respective surface area formulas, and calculate the surface area for each shape.
4. Adjust for overlapping or shared surfaces: If any surfaces are shared or overlapping between the component shapes, subtract the shared surface area from the total surface area to avoid counting it twice. In some cases, you might need to add the area of any newly exposed surfaces that were not part of the original shapes.
5. Sum the surface areas of all component shapes: Add together the surface areas of all the component shapes to find the total surface area of the composite figure.
Example:
Let's say you have a composite 3-D figure consisting of a cube with one face attached to a cylinder. The cube has edge length 4 units, and the cylinder has a height of 7 units and radius of 2 units (the same as half the length of the cube's edge).
1. Break down the figure: Identify that our composite figure consists of a cube and a cylinder.
2. Determine the surface area formulas:
- Cube: SA = 6(s^2) (s = edge length)
- Cylinder: SA = 2πr(r + h) (r = radius, h = height)
3. Calculate the surface area for each component shape:
- Cube: SA = 6(4^2) = 96 square units
- Cylinder: SA = 2π(2)(2 + 7) = 36π square units
4. Adjust for overlapping surfaces: Since one face of the cube is attached to the base of the cylinder, subtract the area of that face (4 * 4 = 16 square units).
5. Sum the surface areas of all component shapes: Total surface area = 96 - 16 (overlapping surface) + 36π = 80 + 36π square units.
How to find the surface area of composite 3-D figures
1 answer