Hi,
I'm on the last question of my homework assignment which is due in a few hours and i'd appreciate it if someone could help me out as i'm not sure how to solve it:
(The question contain two parts - i already solved the first one)
https://i.ibb.co/ckWGj5C/illustration.png
(this is supposed to be a cross-section of a tower)
The first part was to find the volume of the blue section of the tower by rotating around the x-axis.
I solved this by first finding the parabola between BC (rotated 90 degrees) and then finding the volume by rotating it around the x-axis using the equation:
V = π * ∫ f(x)^2 dx
And the way i found the parabola was just by setting up 3 true equations (C is on the parabola, B is on the parabola, and the slope of the parabola at B is 0) and then solving for it.
This next part is the one i'm having trouble with:
Find the volume of the blue part by rotating around the y-axis.
I already know how to rotate around the y-axis - my problem is finding the parabola (when it isn't rotated 90 degrees) since i cant use the third equation because the slope of B would be infinity.
I'm not given any additional information other than whats on the illustration (so i cant assume that C is the highest point of the parabola or anything like that)
If someone knows how to solve this i'd really appreciate it - Thank you.