In the United States, a doll house has the scale of 1:15 of a real house (that i

Question

In the United States, a doll house has the scale of 1:15 of a real house (that is, each length of the doll house is 1/15 that of the real house) and a miniature house (a doll house to fit within a doll house) has the scale of 1:225 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 ,

for the doll house

a) as the scale of real house is 1:15

volume of doll house = length/15 * height/15 * depth/15

volume of doll house = 20/15 * 12/15 * 6/15

volume of doll house = 0.427 m^3

the volume of doll house is 0.427 m^3

b)

for the miniature house

1:225 of real house.

volume of miniature doll house = length/225 * height/225 * depth/225

volume of miniature doll house = 20/225 * 12/225 * 6/225

volume of miniature doll house = 1.26 *10^-4 m^3

the volume of miniature doll house is 1.26 *10^-4 m^3

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