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 a scale of 1: 144 of a real house. suppose a real house (see the figure) has a front length, f=19.0m, a depth, d=10.5m, a height, h=5.5m, and a standard sloped roof(vertical triangular faces on the ends) of height, roof=4.0m.

1) in cubic meters, what is the volume of the doll house?

2)in cubic meters, what is the volume of the miniature house?

(1) The volume of the doll house is 1.96m³

(2) The volume of the miniature house is 1140cm³ = 1.14 × 10^-3 m³

The volume of the house is equal to the area of the cross section of the vertical triangular face of the roof multiplied by the front length of the house. Once the volume of the real house is calculated, to get the volume of the doll house we multiply by a factor of 1/12³ and for the miniature house we multiply by a factor of 1/144³.

Explanation:

The detailed solution can be found in the attachment below. Thank you for reading.

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