🤔 Find out what you don't know with free Quizzes 🤔Start Quiz Now!

WZ

# (a) Cavalieri's Principle states that if a family of parallel planes gives equal cross-section areas for two solids $S_1$ and $S_2$ then the volumes of $S_1$ and $S_2$ are equal. Prove this principle.(b) Use Cavalieri's Principle to find the volume of the oblique cylinder shown in the figure.

## (a) Volume $\left(S_{1}\right)=\int_{0}^{h} A(z) d z=$ Volume $\left(S_{2}\right)$ since the cross-sectional area $A(z)$ at height $z$ is the same for both solids.(b) By Cavalieri's Principle, the volume of the cylinder in the figure is the same as that of a right circular cylinder with radius $r$ and height $h,$ that is, $\pi r^{2} h$

#### Topics

Applications of Integration

### Discussion

You must be signed in to discuss.

Lectures

Join Bootcamp

### Video Transcript

Cavalier is principle states that if a harmony of parallel plays gives equal cross section areas or chew solace as one on as to then the volumes off US one. And as to our vehicle truth, this principle of a part ay we know it's a volume of the solid is equal to the Integral Officer cross area of cross section. So if the heir ears of cross section you call, then inte girl's call isa waddles call for poppy use. Cavalier is Prince Point to find the volume Absar oblique sign. Do show onions a figure. Let's see this figure. We can say it's a volume off this speaker. Is he conscious? Volume after circular cylinder with height Age on DH. Yeah, right. It's old base in secret. You are sayings possibles. Um have the same How it's a pico How serious of cross section Hi are square and we know it's the body. Leo off circular signed er is equal to a high hard squired for base. I was area multiply hat h So this signing Jer But his son neither toh volume is also high. Ask Wayne Sage

WZ

#### Topics

Applications of Integration

Lectures

Join Bootcamp