Step-by-step explanation:
a volume is created (calculated) by multiplying 3 dimensions (e.g. length, width and height).
am area is created by multiplying 2 dimensions (e.g. length and width).
but a scale factor applies only to any length in the model (but then separately for every dimension of the model).
so, when we multiply 2 dimensions, we have to multiply the scale factor with every dimension (2 times) in there too.
and for 3 dimensions 3 times.
so,
1.
the scale factor 1/100 or 0.01 says that every side of the model cube is 1/100 the side length of the real cube.
and so, while the volume of the real cube is
side × side × side = 3,401,244 ft³,
the volume of the model cube is
side × 1/100 × side × 1/100 × side × 1/100 =
= side × side × side × (1/100)³ =
= real volume × 1/1,000,000 =
= 3,401,244 / 1,000,000 = 3.401244 ft³
2.
the scale factor is 3/4.
that means that it applies to length as well as to width of the floor.
so, the area of the first floor is
length × width = 1,260 ft²
and the area of the second floor is then
length × 3/4 × width × 3/4 =
= length × width × (3/4)² =
= area first floor × 9/16 = 1,260 × 9/16 = 708.75 ft²
