Question

similar figures and volume quick check
two similar boxes are used for packaging laundry soap. one box has a volume of 648 inches³, the other box has a volume of 24 inches³. compare the volumes and determine the scale factor between the two boxes. (1 point)
○ 3
○ 1
○ 2
○ ½

Explanation:

Step1: Recall the formula for scale factor of volumes

If two similar solids have a scale factor \(k\), the ratio of their volumes \(V_1\) and \(V_2\) is \(V_1/V_2 = k^{3}\). Let \(V_1 = 648\) and \(V_2=24\). Then \(k^{3}=\frac{V_1}{V_2}\).

Step2: Calculate the ratio of volumes

\(k^{3}=\frac{648}{24}\). Simplify \(\frac{648}{24}=\frac{648\div24}{24\div24} = 27\).

Step3: Find the scale factor

Since \(k^{3}=27\), then \(k=\sqrt[3]{27}\). Because \(3\times3\times3 = 27\), so \(k = 3\).

Answer:

3