What is the volume of a sand pile using double and triple integrals?

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Homework Help Overview

The problem involves calculating the volume of a sand pile defined by a specific region in the xy-plane and a height function. The base is bounded by a parabola and a line, with the height given as a function of x and y. Additionally, there is a question regarding the volume of a cap cut from a solid sphere, requiring the setup of iterated triple integrals in different coordinate systems.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to set up the volume as both double and triple integrals but expresses confusion about how to proceed. Some participants question the initial setup and seek clarification on the methods to approach the problem.

Discussion Status

The discussion is in an early stage, with the original poster indicating a lack of understanding and seeking guidance. One participant has encouraged sharing attempts to facilitate assistance, while another has declined to provide direct solutions.

Contextual Notes

The original poster has expressed difficulty from the beginning and has not provided any specific attempts or reasoning, which may limit the direction of the discussion.

suhaimi
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1- The base of a sand pile covers the region in the xy - plane that is bounded by the parabola
x(power of 2) + y = 6 and the line y = x. The height of the sand above the point (x,y) is x(power of 2).
a) set up the volume of sand as
i) a double integral
ii) a triple integral

b) then, find the volume by using any methods you have found from a)i or a)ii

2- let D be the smaller cap cut from a solid ball a radius 2 units by a plane 1 unit from the center of the sphere.
a) Set up the volume of D as an iterated triple integral in
i) cylindrical coordinate
ii) spherical coordinate

b) then, find the volume by using one of two triple integrals you have found from a)i or a)ii.
 
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Hi suhaimi! Welcome to PF! :smile:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 


I have no Idea to do it. I stuck from beginning. Can you show me how to solve it
 


No. We can't.
 

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