please explain the solution of branch (d) The surfaces r =2 and 4, 0 = 30° and 50°, and = 20° and 60° identify a closed surface.a) Find the enclosed volume: This will ber60°r50°Vol =p2 sin Odrdod = 2.9120°30°where degrees have been converted to radians.b) Find the total area of the enclosing surface:r60°r(sin 30° + sin 50°)drdo20°r60°50°-" |"(4² +22)sin Od0dø +Area =20°J30°50°+2rdrde = 12.6130°c) Find the total length of the twelve edges of the surface:r50°Langth – 1 dr= 4dr + 2(4+2)d0+(4sin50° + 4sin 30° + 2 sin 50° + 2 sin 30°)do230°20°= 17.49d) Find the length of the longest straight line that lies entirely within the surface: This will befrom A(r = 2,0 = 50°, 6 = 20°) to B(r= 4,0 = 30°, o = 60°) orA(x= 2 sin 50° cos20°, y = 2 sin50° sin20°, z = 2 cos 50°)toB(x = 4sin 30° cos60°, y = 4sin 30° sin 60° , z = 4 cos 30°)or finally A(1.44,0.52, 1.29) to B(1.00, 1.73, 3.46). Thus B- A = (-0.44, 1.21, 2.18) andLength = |B – A| = 2.53

Find the length of the longest straight line that lies entirely within the surface: This will from A(r = 2,0 = 50°, ) = 20°) to B(r= 4,0 = 30°, ø = 60°) or A(x: = 2 sin 50° cos20°, y = 2 sin50° sin20°, z = 2 cos 50°) to B(x = 4sin 30° cos60°, y = 4sin 30° sin 60°, z = 4 cos 30°) or finally A(1.44, 0.52, 1.29) to B(1.00, 1.73, 3.46). Thus B – A = (-0.44, 1.21, 2.18) and Length = |B – A| = 2.53

Find the length of the longest straight line that lies entirely within the surface: This will from A(r = 2,0 = 50°, ) = 20°) to B(r= 4,0 = 30°, ø = 60°) or A(x: = 2 sin 50° cos20°, y = 2 sin50° sin20°, z = 2 cos 50°) to B(x = 4sin 30° cos60°, y = 4sin 30° sin 60°, z = 4 cos 30°) or finally A(1.44, 0.52, 1.29) to B(1.00, 1.73, 3.46). Thus B – A = (-0.44, 1.21, 2.18) and Length = |B – A| = 2.53

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 39E: The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle...

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