Question

The dimensions of a room is $10ft\times 8ft\times 8ft$. Calculate the value of the scale factor if the dimensions of the scale model is $20in\times 16in\times 16in$.

• A. $\frac{1}{12}$
• B. $\frac{1}{6}$
• C. $\frac{1}{24}$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $\frac{1}{6}$

The actual dimensions of the room is $10ft\times 8ft\times 8ft$.

The dimensions of the scale model is $20in\times 16in\times 16in$.

$\text{Scale Factor}=\frac{Scale}{Actual}$

$\text{Scale Factor}=\frac{20in\times 16in\times 16in}{10ft\times 8ft\times 8ft}$

$1ft=12in$

$\text{Scale Factor}=\frac{20in\times 16in\times 16in}{(10\times 12)in\times (8\times 12)in\times (8\times 12)in}$

$\text{Scale Factor}=\frac{20}{(10\times 12)}\times \frac{16}{(8\times 12)}\times \frac{16}{(8\times 12)}$

Cross has to be replaced by comma because each dimension has to be calculated separately.

$\text{Scale Factor}=\frac{2}{(1\times 12)},\frac{2}{(1\times 12)},\frac{2}{(1\times 12)}$

$\text{Scale Factor}=\frac{1}{(1\times 6)},\frac{1}{(1\times 6)},\frac{1}{(1\times 6)}$

$\text{Scale Factor}=1\times \frac{1}{6},1\times \frac{1}{6},1\times \frac{1}{6}$

Each dimension has been multiplied by a factor of $\frac{1}{6}$, hence, the scale factor is $\frac{1}{6}$.