Question

the two solids are similar, and the ratio between the lengths of their edges is 2:9. what is the ratio of their surface areas?
a. 64:729
b. 4:81
c. 4:18
d. 8:36

Explanation:

Step1: Recall the surface - area ratio formula

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

Step2: Square the edge - length ratio values

Given the ratio of edge - lengths is \(2:9\). Squaring the values, we get \(2^{2}:9^{2}\).
\[2^{2}=4\]
\[9^{2}=81\]
So the ratio of their surface areas is \(4:81\).

Answer:

B. 4:81