Math Problem about rotating R across the Y axis

Question

Here's the question: https://imgur.com/a/dzrSAVO

I cant solve this question. The setup pi * integral from 0-21 of (7x)^2 - (x)^2 doesn't work. How do I solve it?

Answer 1

Here is the URL to the Desmos graph referenced in the video:

https://www.desmos.com/calculator/0xqu88rwpr

Just select the URL and right click and use Go To.

By the way the solids generated are just cones, so the formula V = 1/3πr²h could have been used, subtracting volume of inner cone from volume of outer cone:

1/3π(21)²(21) - 1/3π(3)²(21) should give same answer as integration solutions.