Çözüldü Cone Volume - Line Equation - Integration

A triangle is formed by the x-axis, the y-axis, and the line y = mx + b. If m = -b^3, then what is the volume of the cone generated by rotating this triangle around the x-axis?

A) π / 9
B) π / 3
C) π
D) 3π
E) 9π

For fun, let us rotate the line about the y-axis and compute the volume by integrating;


https://i72.servimg.com/u/f72/19/97/10/39/fun10.png
https://www.wolframalpha.com/input?i=pi*(integrate ((y-b)/(-b^3))^2 dy from y=0..b)

Considering the choices, b must be taken 1, so the answer is π / 3.

Note: Understanding how the integrand has been written and solving it are of course homework for interested students.

https://images.collegedunia.com/public/college_data/images/entrance/sample_paper/1676286719Math Level 2 SAT Practice Test 15.pdf (The last question)
Geometric Solution: https://www.cracksat.net/sat2/math/question-200-answer-and-explanation.html