Question

a model of a swimming pool has a volume of 0.8 cubic meters, and the scale factor is 1:20. what is the actual volume of the swimming pool in cubic meters? use the keypad to enter your answer in the box. the actual volume of the swimming pool is \boxed{} 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 pool is \(1:20\), so the ratio of the volume of the model to the volume of the actual pool is \(1^{3}:20^{3}=1:8000\). Let \(V_m = 0.8\) (volume of the model) and \(V_a\) (volume of the actual pool). Then \(\frac{V_m}{V_a}=\frac{1}{8000}\).

Step2: Solve for \(V_a\)

From \(\frac{V_m}{V_a}=\frac{1}{8000}\), we can cross - multiply to get \(V_a=V_m\times8000\). Substitute \(V_m = 0.8\) into the equation: \(V_a=0.8\times8000\).

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Answer:

\(6400\)