Question

-25 Points-

Two cylinders are similar. The surface area of one is 64cm^2, and the surface area of the other is 81 cm^2. Find the scale factor between them.

Scale factor =
_ : _

Answer 1

Answer: 8:9

Step-by-step explanation: square root of 64 = 8, square root of 81 = 9, you take square root because it's cm^2

Answer 2

`\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{√(Area)}{√(Area)}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf \cfrac{s}{s}=\cfrac{√(64)}{√(81)}\implies \cfrac{s}{s}=\cfrac{8}{9}\qquad \leftarrow \textit{ratio of the sides or scale factor}`