We want to find the mass of a solid B enclosed within a sphere of radius 2 centred at 5 the origin whose density is given by 8(x, y, z) 1+ (x² + y² + z²)³/2 Recall that the mass of B is given by the triple integral /// 5(x, y, z) dV. Since the B region of integration is spherical, we will use spherical coordinates to carry out our work. (a) What is the density d as a function of spherical coordinates, that is, as a function of p, Ө, and ф? (Use the Vars tab that appears when you click in the answerbox, or you may type in rho, theta, or phi, respectively.) Answer: 8(p, 0, ¢) = (b) In spherical coordinates, the bounds of integration for p, 0, and ø are given by (c) What is the mass of the solid B? (If you enter your answer using a decimal approximation, then round your answer to three decimal places.) mass(B) : to VI
We want to find the mass of a solid B enclosed within a sphere of radius 2 centred at 5 the origin whose density is given by 8(x, y, z) 1+ (x² + y² + z²)³/2 Recall that the mass of B is given by the triple integral /// 5(x, y, z) dV. Since the B region of integration is spherical, we will use spherical coordinates to carry out our work. (a) What is the density d as a function of spherical coordinates, that is, as a function of p, Ө, and ф? (Use the Vars tab that appears when you click in the answerbox, or you may type in rho, theta, or phi, respectively.) Answer: 8(p, 0, ¢) = (b) In spherical coordinates, the bounds of integration for p, 0, and ø are given by (c) What is the mass of the solid B? (If you enter your answer using a decimal approximation, then round your answer to three decimal places.) mass(B) : to VI
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![We want to find the mass of a solid B enclosed within a sphere of radius 2 centred at
5
the origin whose density is given by 8(x, y, z) =
1+ (x² + y² + z²)³/2
Recall that the mass of B is given by the triple integral /|| 8(x, y, z)
dV. Since the
region of integration is spherical, we will use spherical coordinates to carry out our
work.
(a) What is the density d as a function of spherical coordinates, that is, as a function of p,
0, and o?
(Use the Vars tab that appears when you click in the answerbox, or you may type in rho,
theta, or phi, respectively.)
Answer: 6(p, ө, ф) —
(b) In spherical coordinates, the bounds of integration for p, 0, and ø are given by
(c) What is the mass of the solid B? (If you enter your answer using a decimal
approximation, then round your answer to three decimal places.)
mass(B) =
VI](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdce3eaf5-6312-4261-9275-8ca0391d3c33%2F446e0885-bd4b-48a8-9cf6-e33b9827535a%2Fbzki5qi_processed.png&w=3840&q=75)
Transcribed Image Text:We want to find the mass of a solid B enclosed within a sphere of radius 2 centred at
5
the origin whose density is given by 8(x, y, z) =
1+ (x² + y² + z²)³/2
Recall that the mass of B is given by the triple integral /|| 8(x, y, z)
dV. Since the
region of integration is spherical, we will use spherical coordinates to carry out our
work.
(a) What is the density d as a function of spherical coordinates, that is, as a function of p,
0, and o?
(Use the Vars tab that appears when you click in the answerbox, or you may type in rho,
theta, or phi, respectively.)
Answer: 6(p, ө, ф) —
(b) In spherical coordinates, the bounds of integration for p, 0, and ø are given by
(c) What is the mass of the solid B? (If you enter your answer using a decimal
approximation, then round your answer to three decimal places.)
mass(B) =
VI
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