A company manufactures solid objects known as zmoid made of variable density plastic. In the company's design specifications, a zmoid is modelled as a solid region V satisfying the conditions: x² + y² + x² < 1 The mass per unit volume (mass density) of V is ● p(x, y, z) = 102. The point of the zmoid at (0, 0, 0) is referred to as the tip. The company also manufactures the much sought-after deluxe zmoids. These are identical to regular zmoids, except that the part of the zmoid more than 0.9 units from the tip is made of gold rather than plastic. [Note: that the set of all points in a zmoid that are exactly 0.9 units from the tip form part of the surface of a sphere of radius 0.9. This means that the part of a deluxe zmoid made of gold has two spherical boundary surfaces.] ● and Sketch V. Calculate the mass of a Calculate the mass of a z≥ √3(x² + y²). 2 zmoid, using cylindrical coordinates. zmoid, using spherical coordinates.
A company manufactures solid objects known as zmoid made of variable density plastic. In the company's design specifications, a zmoid is modelled as a solid region V satisfying the conditions: x² + y² + x² < 1 The mass per unit volume (mass density) of V is ● p(x, y, z) = 102. The point of the zmoid at (0, 0, 0) is referred to as the tip. The company also manufactures the much sought-after deluxe zmoids. These are identical to regular zmoids, except that the part of the zmoid more than 0.9 units from the tip is made of gold rather than plastic. [Note: that the set of all points in a zmoid that are exactly 0.9 units from the tip form part of the surface of a sphere of radius 0.9. This means that the part of a deluxe zmoid made of gold has two spherical boundary surfaces.] ● and Sketch V. Calculate the mass of a Calculate the mass of a z≥ √3(x² + y²). 2 zmoid, using cylindrical coordinates. zmoid, using spherical coordinates.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![A company manufactures solid objects known as zmoid made of variable density
plastic. In the company's design specifications, a zmoid is modelled as a solid region V satisfying
the conditions:
z ≥ √3(x² + y²).
x² + y² + z² ≤ 1
The mass per unit volume (mass density) of V is
p(x, y, z) = 10z.
The point of the zmoid at (0, 0, 0) is referred to as the tip.
The company also manufactures the much sought-after deluxe zmoids. These are identical to
regular zmoids, except that the part of the zmoid more than 0.9 units from the tip is made of
gold rather than plastic. [Note: that the set of all points in a zmoid that are exactly 0.9 units
from the tip form part of the surface of a sphere of radius 0.9. This means that the part of a
deluxe zmoid made of gold has two spherical boundary surfaces.]
Sketch V.
• Calculate the mass of a
●
Calculate the mass of a
●
●
and
●
zmoid, using cylindrical coordinates.
zmoid, using spherical coordinates.
Determine the exact volume of gold required to manufacture 1,000 deluxe zmoids.
Assuming that gold has a constant density (mass per unit volume) of 19, use the MATLAB
symbolic toolbox to calculate the mass of a deluxe zmoid.
[Use spherical coordinates.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12fdac56-4b52-4434-8b00-5772085cd8ad%2Feccece12-ac2d-4fc5-af88-85932a86a59e%2F8hd79y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A company manufactures solid objects known as zmoid made of variable density
plastic. In the company's design specifications, a zmoid is modelled as a solid region V satisfying
the conditions:
z ≥ √3(x² + y²).
x² + y² + z² ≤ 1
The mass per unit volume (mass density) of V is
p(x, y, z) = 10z.
The point of the zmoid at (0, 0, 0) is referred to as the tip.
The company also manufactures the much sought-after deluxe zmoids. These are identical to
regular zmoids, except that the part of the zmoid more than 0.9 units from the tip is made of
gold rather than plastic. [Note: that the set of all points in a zmoid that are exactly 0.9 units
from the tip form part of the surface of a sphere of radius 0.9. This means that the part of a
deluxe zmoid made of gold has two spherical boundary surfaces.]
Sketch V.
• Calculate the mass of a
●
Calculate the mass of a
●
●
and
●
zmoid, using cylindrical coordinates.
zmoid, using spherical coordinates.
Determine the exact volume of gold required to manufacture 1,000 deluxe zmoids.
Assuming that gold has a constant density (mass per unit volume) of 19, use the MATLAB
symbolic toolbox to calculate the mass of a deluxe zmoid.
[Use spherical coordinates.]
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