Miscellaneous volumes Choose the best coordinate system for finding the volume of the following solids. Surfaces are specified using the coordinates that give the simplest description, but the simplest integration may be with respect to different variables. 66. That part of the ball ρ ≤ 2 that lies between the cones φ = π /3 and φ = 2 π /3
Miscellaneous volumes Choose the best coordinate system for finding the volume of the following solids. Surfaces are specified using the coordinates that give the simplest description, but the simplest integration may be with respect to different variables. 66. That part of the ball ρ ≤ 2 that lies between the cones φ = π /3 and φ = 2 π /3
Solution Summary: The author explains that the volume of the solid is 16pi3. The region is the part of a ball and lies between the cones.
Miscellaneous volumesChoose the best coordinate system for finding the volume of the following solids. Surfaces are specified using the coordinates that give the simplest description, but the simplest integration may be with respect to different variables.
66. That part of the ball ρ ≤ 2 that lies between the cones φ = π/3 and φ = 2π/3
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Find the volume of the solid generated by revolving the region bounded by the graphs of the
following equations about the indicated line. Draw a picture of the region to be rotated along with
a representative rectangle. Clearly indicate the METHOD that you are using. Give a brief
explanation of why you chose to use that particular method. Then, find the volume.
y= x^2, y= 2x, about the line x= -2.
Solid bounded in the 1st octant by coordinate planes, the plane y+z=2, and the cylinder x=4-y^2. Set up the following order of integration: dzdydx and dydzdx (this order requires 2 triple integarals).
A tank has a shape of a cone with a radius at the top of 2 m and a height of 7 m. The tank also has a 2 m spout at the top of the tank. The tank is filled with water up to a height of 2 m. Find the work needed to pump all the water out the top of the spout. (Use 9.8 m/s2 for g and the fact that the density of water is
1000 kg/m3.)
Chapter 16 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY