Question

1. a cylinder with a surface area of 800 cm² is reduced to produce a similar cylinder with a surface area of 8 cm². what scale factor was used to make this reduction?

Explanation:

Step1: Recall the relationship of surface - areas and scale factor

If the scale factor of two similar solids is \(k\), the ratio of their surface - areas \(A_1\) and \(A_2\) is \(k^{2}\), i.e., \(\frac{A_2}{A_1}=k^{2}\), where \(A_1\) is the surface - area of the original solid and \(A_2\) is the surface - area of the new solid. Let the original surface - area \(A_1 = 800\ cm^{2}\) and the new surface - area \(A_2=8\ cm^{2}\).

Step2: Calculate the square of the scale factor

We have \(k^{2}=\frac{A_2}{A_1}\). Substitute \(A_1 = 800\ cm^{2}\) and \(A_2 = 8\ cm^{2}\) into the formula: \(k^{2}=\frac{8}{800}=\frac{1}{100}\).

Step3: Find the scale factor

Take the square - root of \(k^{2}\). Since \(k^{2}=\frac{1}{100}\), then \(k=\sqrt{\frac{1}{100}}=\frac{1}{10}\).

Answer:

\(\frac{1}{10}\)