Question

Ballast tanks are used to store seawater for the functioning of a submarine. The volume of the main ballast tank of a submarine is $49m^3.$ A scale model is adopted for the submarine's design with a scale factor of $1:7.$ Find the volume of model of the main ballast tank.

• A. $7m^3$
• B. $\frac{1}{7}{m}^3$
• C. $\frac{1}{49}{m}^3$

Answer 1

The correct option is B $\frac{1}{7}{m}^3$

When we calculate volume of any three dimensional object, we use three dimensions $(\text{length}\times \text{width}\times \text{height},{\text{side}}^3...\text{etc.})$ to determine the volume.

If the scale factor is $k$, then each of these three dimensions must be multiplied by $k$ to find the dimensions for the new object.

$\therefore$ Volume of model $=(k\times \text{length})\times (k\times \text{width})\times (k\times \text{height})$
$=k\cdot k\cdot k\times (\text{length}\times \text{width}\times \text{height})$
$=k^3\times \left(\text{volume of the original object}\right)$

Here, the scale factor is $1:7=\frac{1}{7}$.

$\therefore$ Volume of the model

$=(\frac{1}{7}{)}^3\times \text{volume of the original object}$
$=\frac{1}{7\times 49}\times 49m^3$
$=\frac{1}{7}{m}^3$