Question

question 4 of 10
if two pyramids are similar and the ratio between the lengths of their edges is 2:7, what is the ratio of their volumes?
a. 4:49
b. 49:4
c. 8:343
d. 2:7

Explanation:

Step1: Recall volume - ratio formula for similar solids

For two similar solids, if the ratio of their corresponding linear dimensions (such as edge - lengths) is \(a:b\), the ratio of their volumes is \(a^{3}:b^{3}\).

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

Here, \(a = 2\) and \(b = 7\) since the ratio of the lengths of their edges is \(2:7\).

Step3: Calculate \(a^{3}\) and \(b^{3}\)

\(a^{3}=2^{3}=8\) and \(b^{3}=7^{3}=343\). So the ratio of their volumes is \(8:343\).

Answer:

C. 8:343