Question

(1 point) A bead is made from material with constant density 5 grams per cubic millimeter by drilling a cylindrical hole of radius 1 mm through a sphere of radius 5 mm (a) Set up a triple integral in cylindrical coordinates representing the mass of the bead in grams (do not include units) If necessary, enter 0 as theta dz dr de = APf Bead A = B= C = D = E = F= Enable Java to make this image interactive (b) Find the mass of the bead (Drag to rotate) grams

Answer 1

Solution: bead made tnom a mateial ob constant density let the P 5 Tadius of the spheue i 6 me and the vodius of the cybndical base is mm The equation of spheve of madius 5 given by cybndlorical o-aydmales and y 3Cose, y Sine / dv: adz ddo So he spheore m cylindouical co-oudimales gives 25 zt/95- toriple mlegoral tomass o the bead i LT5 t/25- F dv so The Td dde Bead 15- 5 JIJ Fdv Dcad 35-9 53dzdrdo J I -25- 0 A O D= 5 05-0 E:- F-+a5-7

95-0V mass 51 dz dr do fas- 25-7 Tddo 25- 0 5 95- 95-0 10 /95-/ddo / do 2 10 (-1) Jap |(06-54 2T do 3 0 3 () 10 y(34) 0 (34), ) =391.9 783.8