AP® Calculus BC · Unit 8 · Topic 8.8
Volumes with Cross Sections: Triangles and Semicircles
Watch it explained
- How it worksHow does a semicircle standing on a chord turn into π over 8 times that chord squared?
- Worked exampleFind the volume of a solid with equilateral triangle cross sections over the region under y = 4 - x2.
- Common mistakeWhy doesn't the semicircle's radius equal the full distance between the two curves?
- Going furtherWhat happens to the volume formula when the cross sections are isosceles right triangles?
Check yourself
Your turn1 of 2
Find the volume of a solid with equilateral triangle cross sections standing on the region under y = 5 - x2 (down to the x-axis).End of topic.