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# The base of $S$ is a circular disk with radius $r$. Parallel cross-sections perpendicular to the base are isosceles triangles with height $h$ and unequal side in the base. (a) Set up an integral for the volume of $S$. (b) By interpreting the integral as an area, find the volume of $S$.

## a) $V=2 h \int_{0}^{r} \sqrt{r^{2}-x^{2}} d x$b) $V=\frac{1}{2} \pi r^{2} h$

#### Topics

Applications of Integration

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##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

The problem is base of ice is a circular disk with writers are parallel cross sections and vehicular to the base. A. Celeste strangles with height, age on Deke aside into base a setup an integral for the volume of US B. But into present, integral as an area find is a volume of ice. So for this problem, first, let's look at the graph here for any cross section. It is triangle on DH. If I didn't know that the distance between Thiss cross section on the Y axis is equal to X than the base of this cross section is he can chew two halves a squared, minus X koi. So the area of the cross section is the CO two half. I'm such hands, too. Notify our square. My psych score. This is it. It's our squire. Lina sacks coy. Then the volume of the sonnet is the culture shoot times into Girl from Cyril, You are and hands. Let's have our squire minds Act square. Yes, this's control to H into girl from zero. You are beautiful. Our squire minus exclaim the x for part B. Notice that the integral from zero to our return our score months. Exploiter is area off Carter Circle. Where's the riders are? That's an integral of ground zero To our narrative are square mints. Exploiter is equal to by force. Hi are square, so leave It's called to age terms. Our force high are squares with Gunther is well, half hands itch Spy, uh, score.

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#### Topics

Applications of Integration

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp