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## Integral Calculus

### Unit 3: Lesson 7

Volume: squares and rectangles cross sections

# Volume with cross sections perpendicular to y-axis

AP.CALC:
CHA‑5 (EU)
,
CHA‑5.B (LO)
,
CHA‑5.B.1 (EK)
Worked example expressing the volume of a figure based on cross sections perpendicular to the y-axis as a definite integral (integrating with respect to y).

## Want to join the conversation?

• What is the answer to this problem so I can double check my work?
• Are there any practice problems with these y-axis perpendicular cross sections?
• What if the height of the cross sections is y^2 and not only y? How to approach such a problem.
• Nothing about the process changes, we still find the "volume" of one of the cross sections and use that to construct our integral. It just happens that this time, because the height of the cross section is y^2 instead of y, the volume of one cross section will be y^2 * x * dy. After writing x in terms of y, same as in the video, the final integral should be the integral of y^2 * (9 - y^2/16)dy, from 0 to 12.