Question

Seth has two similar ice-cream cones, Cone A and Cone B. The slant height of Cone A is 16 inches, and the slant height of Cone B is 4 inches. What is the ratio of the volume of Cone A to the volume of Cone B?
64 : 1

8 : 1

4 : 1

16 : 1

Answer 1

Answer:

64:1

Step-by-step explanation:

For similar lengths, we use the relationship  $A=kB$ where A and B are the measurements of the two figures' lengths and k is the scale factor.

For similar volumes, we use the relationship  $A=k^3B$ where A and B are the measurements of the two figures' volumes and k is the scale factor.

Since lengths are given, we use the first formula to find k:

$16=k(4)\\k=\frac{16}{4}=4$

The 2nd formula also tells us that volumes are $k^3$ of each other. So

$k^3=(4)^3=64$

That means the larger cone has a volume that is 64 times the smaller. So the ratio is 64:1

Answer 2

The ratio of the volume of Cone A to the volume of Cone is 64 : 1. The correct answer between all the choices given is the first choice. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.