We want to find the mass of a solid B enclosed within a sphere of radius 2 centred at5the origin whose density is given by 8(x, y, z) =1+ (x² + y² + z²)³/2Recall that the mass of B is given by the triple integral /|| 8(x, y, z)dV. Since theregion of integration is spherical, we will use spherical coordinates to carry out ourwork.(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 decimalapproximation, then round your answer to three decimal places.)mass(B) =VI

Answered: Image /qna-images/answer/446e0885-bd4b-48a8-9cf6-e33b9827535a.jpg

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

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 5E: For the right circular cylinder, suppose that r=5 in. and h=6 in. Find the exact and approximate a...

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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

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