Question

question 18 of 25
two similar cones have radii of 9 and 1, respectively. what is the ratio of their volumes?
a. 81:1
b. 729:1
c. 781:1
d. 18.85:1

Explanation:

Step1: Recall the volume formula for similar solids

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

Step2: Identify the ratio of the radii

The ratio of the radii of the two similar cones is \(r_1:r_2 = 9:1\).

Step3: Calculate the ratio of the volumes

Using the formula for the ratio of volumes of similar solids (\(V_1:V_2=(r_1:r_2)^{3}\)), we substitute \(r_1 = 9\) and \(r_2 = 1\). Then \(V_1:V_2=(9:1)^{3}=\frac{9^{3}}{1^{3}}=\frac{729}{1}\). So the ratio of their volumes is \(729:1\).

Answer:

B. \(729:1\)