Final answer:
To calculate the total outside surface area of geometric shapes, use shape-specific formulas. For volume, different formulas based on the geometry of the solid are used. Dimensional analysis assists in converting between units of area and volume.
Step-by-step explanation:
To find the total outside surface area of various geometric shapes, different formulas are applied based on the shape in question. For example, the surface area of a cube is calculated by multiplying the area of one face (s²) by six because a cube has six identical faces.
Therefore, the surface area (SA) of a cube can be given as SA = 6s². Similarly, for cylinders, we must consider not only the areas of the two circular end-caps (πr²) but also the area of the rectangular side that wraps around the cylinder, which is the product of the circumference of the circle (2πr) and the height (h) of the cylinder. Hence, the total surface area of a cylinder is calculated as SA = 2πr² + 2πrh.
As for volume, it is the amount of space enclosed within a solid. The volume of a cube is the cube of its side's length (V = s³), whereas the volume of a cylinder is found by multiplying the base area (πr²) by the height (V = πr²h).
Dimensional analysis can be applied to convert between different unit measurements of area and volume. For instance, to convert cm² to m², one can use the relation that 1 cm² = (10⁻² m)² = 10⁻⁴ m².