The two cones are similar. the ratio of their surface areas is 13.69/4
find the volume of the small cone is 433.54 in^3
true or false? ?

2745.0127025 or 68.472153673

Step-by-step explanation:

So we know that the ratio of a line to area to volume is x/y , x^2/y^2, x^3/y^3. Knowing one of these ratios and one of the volume can help us easily find the volume.

First we have to convert x^2/y^2 to x/y, so the square root of 13.69/4, which gives us 3.7/2. Then we cube this to get the volume ratio of 50.653/8.

Now to where I got two answers.

I wasn't sure if 433.54 in^3 was the bigger volume or the smaller one, so I solved for both. Assuming it's the bigger volume, the volume of the smaller cone would be 68.472153673, if it's the bigger cone it would be 2745.0127025.

For the true or false question, the radius of the smaller one was 20.34, and if you divide that by 11.1 and compare it to 3.7/2 they are extremely close (1.83 to 1.85) So i would say it's true