3D Shapes- Surface area
3D Shapes- Surface area
Understanding 3D Shapes
- 3D shapes have three dimensions: length, width, and height.
- Common examples include cubes, cuboids, cylinders, cones, spheres, and pyramids.
Surface Area of 3D Shapes
- The surface area of a 3D shape is the total area of all its outer surfaces.
- Different shapes have different formulas to calculate their surface area.
Surface Area of Cubes and Cuboids
- A cube is a regular shape which has all its sides of equal length while a cuboid has different dimensions.
- A cube has six equal square faces, so to find its surface area, multiply the area of one face (side length squared) by 6.
- For a cuboid, calculate the area of each face (2 of each shape: top/bottom, front/back, left/right), and add them up for the total surface area.
Surface Area of Cylinders
- A cylinder has two circular faces and one curved face.
- To calculate the surface area, add the area of the two circles (πr²) to the area of the rectangle that would be formed if the curved surface was unrolled (2πrh).
Surface Area of Cones and Pyramids
- Cones and pyramids have a base (which can be a range of shapes) and a curved or slanting surface.
- To calculate the surface area of a cone, add the area of the base (πr²) to the area of the side (πrL), where L is the slant height.
- For a pyramid, add the area of the base to the total area of the triangular faces.
Surface Area of Spheres
- A sphere has one continuous curved surface. The surface area is calculated by the formula 4πr².
Applying Surface Area in Real-Life
- Understanding how to compute surface area is essential in many real-life applications, from packaging and construction to sports equipment design and aerodynamics.