Question

the two solids below are similar, and the ratio between the lengths of their edges is 3:5. what is the ratio of their surface areas? a. 9:15 b. 5:3 c. 27:125 d. 9:25

Explanation:

Step1: Recall the surface - area ratio formula

For two similar solids with a scale factor (ratio of corresponding edge - lengths) of \(a:b\), the ratio of their surface areas is \(a^{2}:b^{2}\).

Step2: Identify \(a\) and \(b\)

Here, the ratio of the lengths of their edges is \(3:5\), so \(a = 3\) and \(b = 5\).

Step3: Calculate the ratio of surface areas

We find \(a^{2}:b^{2}=3^{2}:5^{2}=9:25\).

Answer:

D. 9:25