# hmwk7 - Math 215 Homework Set 7 16.7 17.2 Winter 2008 Most...

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Math 215 Homework Set 7: §§ 16.7 – 17.2 Winter 2008 Most of the following problems are modified versions of the recommended homework problems from your text book Multivariable Calculus by James Stewart. 16.8a. Find the volume of one of the smaller wedges cut from a sphere of radius 27 by two planes that intersect along a diameter at an angle of π / 6 . 16.8b. Find the volume and center of mass of the solid that lies above the cone z = 3 x 2 + y 2 and below the sphere x 2 + y 2 + z 2 = 9 . Assume that the density of the solid is constant. 16.8c. Find the volume of the solid that lies above the cone ϕ = π / 3 and below the sphere ρ = 9 cos( ϕ ) . 16.8d. Evaluate B (3 x 2 + 3 y 2 + 3 z 2 ) dV where B is the ball of radius 13 centered at the origin. 16.8e. Find the center of mass of a solid hemisphere of radius 5 if the density at any point in the hemisphere is proportional to the point’s distance from the base of the hemisphere. 16.8f. Do Problems 27–28 of § 16.7 39 and 40 of § 16.8 in Stewart’s Multivariable Calculus .

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