Question

question 23 of 25
the ratio of the surface areas of two similar solids is 16:144. what is the ratio of their corresponding side lengths?
a. 4:144/4
b. 4:12
c. 1:96
d. 16/12:12

Explanation:

Step1: Recall the formula for the ratio of surface areas of similar solids

For two similar solids, if the ratio of their surface areas is \(S_1:S_2\), and the ratio of their corresponding side lengths is \(a:b\), then \(S_1:S_2=a^{2}:b^{2}\). Given \(S_1:S_2 = 16:144\).

Step2: Find the ratio of side lengths

Let \(a^{2}=16\) and \(b^{2}=144\). Then \(a=\sqrt{16} = 4\) and \(b=\sqrt{144}=12\). So the ratio of their corresponding side lengths \(a:b = 4:12\).

Answer:

B. \(4:12\)