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

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 = 24 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 = 3.6 m. (a) What is the volume of the corresponding doll house in cubic meters? m^3 (b) What is the volume of the corresponding miniature house in cubic meters? m^3

Explanation / Answer

the doll house dimensions are:

front length = 24/12 = 2 m

depth = 12/12 = 1 m

height = 6/12 = 0.5 m

attic height = 3.6/12 = 0.3

miniature house dimensions are

front length = 24/144 = 0.167 m

depth = 12/144 = 0.083 m

height = 6/144 = 0.042 m

attic height = 3.6/144 = 0.025

V = Length x depth x height

V(attic) = 1/2 x Length x depth x height

V(doll house) = 2 x 1 x 0.5 = 1 m^3

attic(doll house) = 1/2 x 2 x 1 x 0.3 = 0.3 m^3

V = 1 + 0.3 = 1.3 m^3

V(mini) = 0.167 x 0.083 x 0.042 = 0.00058 m^3

V(attic-mini) = 1/2 x 0.167 x 0.083 x 0.025 = 0.00017 m^3

V(mini) = 0.00075 m^3

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.