Question

seth has two similar ice - cream cones, cone a and cone b. the height of cone a is 16 inches, and the height of cone b is 4 inches. what is the ratio of the volume of cone a to the volume of cone b? 16:4 4:1 12:3 64:1

Explanation:

Step1: Recall volume formula for similar cones

For two similar cones, if the ratio of their corresponding linear - dimensions (such as height) is \(a:b\), the ratio of their volumes is \(a^{3}:b^{3}\). Here, the ratio of the height of Cone A to Cone B is \(h_A:h_B = 16:4=4:1\).

Step2: Calculate volume ratio

Since the ratio of volumes of two similar solids is the cube of the ratio of their corresponding linear - dimensions, if the ratio of the heights (linear - dimensions) is \(4:1\), the ratio of the volumes \(V_A:V_B=(4)^{3}:(1)^{3}=64:1\).

Answer:

64:1