Question

a water tank has an actual volume of 500 cubic meters. you are creating a scale model with a scale factor of 1:10. what is the volume of the model in cubic meters? use the keypad to enter your answer in the box. the volume of the model is □ cubic meters.

Explanation:

Step1: Recall the volume - scale factor relationship

If the scale factor of two similar solids is \(a:b\), the ratio of their volumes is \(a^{3}:b^{3}\). Here, the scale factor of the model to the actual tank is \(1:10\), so the ratio of the volume of the model (\(V_m\)) to the volume of the actual tank (\(V_a\)) is \(1^{3}:10^{3}=1:1000\). Mathematically, \(\frac{V_m}{V_a}=\frac{1^{3}}{10^{3}}\).

Step2: Solve for the volume of the model

We know that \(V_a = 500\) cubic meters. Substitute \(V_a\) into the formula \(\frac{V_m}{V_a}=\frac{1}{1000}\). Then \(V_m=\frac{V_a}{1000}\).
Substitute \(V_a = 500\) into the equation: \(V_m=\frac{500}{1000}\).

Answer:

\(0.5\)