Final answer:
The concept that includes finding the total external area of three-dimensional objects like boxes and prism-based structures is the calculation of surface area, which applies to different shapes, including cuboids, prisms, and pyramids. So, the correct answer is 4) All of the above.
Step-by-step explanation:
The mathematical concept that encompasses determining the total external area of three-dimensional objects such as rectangular boxes, parallelepipeds, and structures with polygonal bases is finding the surface area.
This includes finding the surface area of cuboids, prisms, and pyramids.
For instance, to calculate the surface area of a cylinder, which is a type of prism, you would need to find the area of the two circular end-caps (each πr²) and the area of the rectangle that forms the curved surface (2πrh).
It's important to remember that when struggling with complex formulas, you can always rely on basic geometrical shapes and units.
In the case of a cylinder, we use elements of circular and rectangular geometries.
The same applies to other shapes like spheres and cubes, where the volume of a sphere is given by 4/3 (π) (r)³ and the surface area by 4 (π) (r)², while for a cube, the volume is (s)³ and the surface area is 6 (s)².
Thus, the correct answer is 4) All of the above.
Which mathematical concept encompasses determining the total external area of different three-dimensional objects, including rectangular boxes, parallelepipeds, and structures with polygonal bases?
1) Finding the surface area of cuboids
2) Finding the surface area of prisms
3) Finding the surface area of pyramids
4) All of the above