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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
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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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
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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