Question

the scale factor of a large milk container to a small milk container is 0.08. the large milk container can carry 12,000cm³ of milk. how much milk can the small container carry? 0.08 cm³ 960 cm³ 6.144 cm³ 76.8 cm³

Explanation:

Step1: Recall volume - scale - factor relationship

If the scale factor of two similar solids is \(k\), the ratio of their volumes is \(k^{3}\). Here, \(k = 0.08\), and the volume of the large container \(V_{l}=12000\ cm^{3}\), and we want to find the volume of the small container \(V_{s}\). The relationship is \(\frac{V_{s}}{V_{l}}=k^{3}\).

Step2: Calculate \(k^{3}\)

\(k^{3}=(0.08)^{3}=0.08\times0.08\times0.08 = 0.000512\)

Step3: Find \(V_{s}\)

Since \(\frac{V_{s}}{V_{l}}=k^{3}\), then \(V_{s}=V_{l}\times k^{3}\). Substitute \(V_{l} = 12000\ cm^{3}\) and \(k^{3}=0.000512\) into the formula: \(V_{s}=12000\times0.000512 = 6.144\ cm^{3}\)

Answer:

C. \(6.144\ cm^{3}\)