Question

John has the blueprint of a room designed with a scale factor of $1:12.$ The dimensions of the room on the blueprint are
$(10\times 8\times 12)$ cubic inches.
Find the actual dimension of the room.

• A. $9600\text{cu ft}$
• B. $1658.8\text{cu ft}$
• C. $16588\text{cu ft}$
• D. $960\text{cu ft}$

Answer 1

The correct option is D $960\text{cu ft}$

Dimensions of the room on the blueprint $=10in\times 8in\times 12in$
Scale factor $=\frac{1}{12}$
We know that,
$\text{Scale factor}=\frac{\text{dimension of scaled model}}{\text{dimension of actual object}}$
$\Rightarrow \text{Dimension of actual object}=\frac{\text{dimension of scaled model}}{\text{scale factor}}$
$=\frac{\text{dimension of scaled model}}{\left(\frac{1}{12}\right)}$
$=\text{dimension of scaled model}\times 12$
Hence, the actual dimensions can be found by multiplying the corresponding dimensions of the room on the blueprint by $12.$
$\Rightarrow (10in\times 12)\times (8in\times 12)\times (12in\times 12)$
$=(120\times 96\times 144)cuin$

But, we need the dimensions in feet.
We know, $12in=1ft$
Hence, the actual dimensions in feet will be
$(\frac{120}{12}\times \frac{96}{12}\times \frac{144}{12})cuft$
$=(10\times 8\times 12)cuft$
$=960cuft$