Question

question 8 of 25
the ratio of the lengths of corresponding parts in two similar solids is 4:1. what is the ratio of their surface areas?
a. 8:1
b. 4:1
c. 16:1
d. 64:1

Explanation:

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

The ratio of the surface areas of two similar solids is the square of the ratio of their corresponding linear dimensions. If the ratio of corresponding lengths is \(a:b\), the ratio of surface areas is \(a^{2}:b^{2}\).

Step2: Apply the formula

Given the ratio of corresponding lengths \(a:b = 4:1\). Then the ratio of surface areas is \(a^{2}:b^{2}=4^{2}:1^{2}\).

Calculate \(4^{2}=16\) and \(1^{2} = 1\). So the ratio of their surface areas is \(16:1\).

Answer:

C. 16:1