In the United States, a doll house has the scale of 1:16 of a real house (that i

Question

In the United States, a doll house has the scale of 1:16 of a real house (that is, each length of the doll house is 1/16 that of the real house) and a miniature house (a doll house to fit within a doll house) has the scale of 1:256 of a real house. Suppose a real house (see the figure) has a front length of 20 m, a depth of 12 m, a height of 6.0 m, and a standard sloped roof (vertical triangular faces on the ends) of height 3.0 m. What are the volumes of the corresponding (a) doll house and (b) miniature house?

Explanation / Answer

here

doll house = 1 : 16

miniature house = 1 : 256

length l = 20 m

width w = 12 m

h1 = 6 m

h2 = 3 m

V1 = h1 * w * l

V2 = 0.5 * h2 * w *l

V = V1 + V2

V = (h1 + 0.5 h2 ) w * l

V = ( 6 + 0.5 * 3 ) 12 * 20

V = 1800 m^3

a)

volume of doll house Vd = V / 16^3

Vd = 1800 / 4096 = 0.44 m^3

so the volume of the doll house is 0.44 m^3

b)

miniature house

Vm = V / 256^3

Vm = 1800 / 16777216 = 0.0001072 m^3

so the volume of the miniature house is 1.07 * 10^-4 m^3

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