In the United States, a doll house has the scale of 1:12 of a real house (that i

Question

In the United States, a doll house has the scale of 1:12 of a real house (that is, each length of the doll house is 1/12 that of the real house) and a miniature house (a doll house to fit within a doll house) has the scale of 1:144 of a real house. Suppose a real house (see figure below) has a front length of L = 21 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 h = 2.6 m.

(a) What is the volume of the corresponding doll house in cubic meters?
m3

(b) What is the volume of the corresponding miniature house in cubic meters?
m3

Explanation / Answer

a) dimensions of doll house :

length = 21/12=1.75 m

width = 12/12=1 m

height = 6/12=0.5m

sloped roof height = 2.6/12=0.2167 m

volume of doll house = (1.75*1*0.5)+(0.5*1*0.2167*1.75)=1.065 m3

b) Dimensions of miniature house:

length = 21/144=0.146 m

width = 12/144=0.083 m

height = 6/144=0.04167 m

sloped roof height = 2.6/144=0.018 m

Volume of miniature house = (0.146*0.083*0.04167) + (0.5*0.083*0.04167*0.146) = 0.000757 m3

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