91影视

The length of the house,$\mathrm{I}=20\mathrm{m}$

The depth of the house,$\mathrm{d}=12\mathrm{m}$

The height of the house, $\mathrm{h}=6.0\mathrm{m}$

The height of the roof, ${\mathrm{h}}^1=3.0\mathrm{m}$

The volume is the space enclosed by a three dimensional object. In this problem, the total volume of the real house is that of a triangular prism in addition to a rectangular box.

The expression for the volume of a rectangular box is given as:

$\mathrm{V}=\mathrm{I}脳\mathrm{d}脳\mathrm{h}$ 鈥� (i)

Here,$\mathrm{I}$is the length, d is the breadth and h is the height.

The expression for the volume of triangular prism is given as:

$\mathrm{V}=\frac{1}{2}\left(\mathrm{I}脳\mathrm{d}脳\mathrm{h}\right)$鈥� (ii)

Assume that the volume of the sloped roof is ${\mathrm{v}}_{\mathrm{R}}$ and the volume of the box is ${\mathrm{v}}_{\mathrm{B}}$. The total volume $\mathrm{V}$ of the real house is sum of both the volumes.

$$\begin{gathered} \mathrm{V}={\mathrm{v}}_{\mathrm{R}}+{\mathrm{v}}_{\mathrm{B}} \\ =\frac{1}{2}\left(\mathrm{I}脳\mathrm{d}脳{\mathrm{h}}^1\right)+\left(\mathrm{I}脳\mathrm{d}脳\mathrm{h}\right) \end{gathered}$$

Substitute the values in the above equation.

$$\begin{gathered} \mathrm{V}=\left(\frac{1}{2}脳20\mathrm{m}脳12\mathrm{m}脳3.0\mathrm{m}\right) \\ =360{\mathrm{m}}^3+1440{\mathrm{m}}^3 \\ =1800{\mathrm{m}}^3 \end{gathered}$$

Thus, the volume of the real house is $1800{\mathrm{m}}^3$

As the doll house is made with the ratio of 1:12, it means each dimension is reduced by the factor$\frac{1}{12}$. So, the volume of doll house is reduced by ${\left(\frac{1}{12}\right)}^3$.

The volume of the doll house is calculated as:

$$\begin{gathered} {\mathrm{V}}_{\mathrm{Dd}\mathrm{house}}=\mathrm{V}脳{\left(\frac{1}{12}\right)}^3 \\ =1800{\mathrm{m}}^3脳{\left(\frac{1}{12}\right)}^3 \\ =1.0{\mathrm{m}}^3 \end{gathered}$$

Thus, the volume of the doll house is $1.0{\mathrm{m}}^3$.

As the miniature house is made with the ratio $1:144$, it means each dimension is reduced by the factor $\frac{1}{144}$. So, the volume is reduced by ${\left(\frac{1}{144}\right)}^3$.

The volume of the miniature house is calculated as:

$$\begin{gathered} {\mathrm{V}}_{\mathrm{miniature}\mathrm{House}}=\mathrm{V}脳{\left(\frac{1}{144}\right)}^3 \\ =1800{\mathrm{m}}^3脳\left(\frac{1}{144}\right) \\ =6.0脳{10}^{鈥�4}{\mathrm{m}}^3 \end{gathered}$$

Thus, the volume of the miniature hours is $6.0脳{10}^{鈥�4}{\mathrm{m}}^3$.