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Is the integral of the volume of a cone the volume (or equivalent) of a shape projected in a 4th dimension?
I am computing the volume of the cone $x^2+z^2=y^2$, truncated at $y=1$ and $y=3$ with three different methods: $V=V(\text{big cone})-V(\text{small cone})=9\pi - \pi/3 = 26\pi/3$, where I used the formula $V(\text{cone})=\pi r^2 h/3$, $r$ being the radius of the basis of the cone, and $h$ its height.
22 paź 2018 · Determine the volume of a solid by integrating a cross-section (the slicing method). Find the volume of a solid of revolution using the disk method. Find the volume of a solid of revolution with a cavity using the washer method.
21 mar 2020 · If I have a cone $z=\sqrt{x^2+y^2}$ located between $z=0$ and $z=1$, its volume is NOT the following integral: $$V=\int_{-1}^{1}dx\int_{-\sqrt{1-x^{2}}}^{\sqrt{1-x^{2}}}dy\int_{0}^{1}dz$$ Below you can see the graph of that cone
We can use a definite integral to find the volume of a three-dimensional solid of revolution that results from revolving a two-dimensional region about a particular axis by taking slices perpendicular to the axis of revolution which will then be circular disks or washers.
18 lis 2015 · In this video I find the exact volume of a cone by using integration. ...more. Visit http://ilectureonline.com for more math and science lectures!
9 sty 2009 · What is the volume of a truncated cone with a circular base of radius r. 1and circular top of radius r. 2(with the top parallel to the base)? 2.4 Drag: Using dimensions and easy cases.
