Question

10.0 mm 3) A bullet (shown in figure) consists of a cylinder and a paraboloid of revolution and is made of lead having a density of 11.3 g/cm3. Use the method of integrals find the volume of paraboloid. Then calculate the total mass of the bullet in grams. Round your final answer to 3 significant digits. [4 marks] 12.0 mm 14.0 mm

Answer 1

3 is mnt toun 12 mm 22 choose origin at tip of bullet- the paraboloid portiam defined by Z in cylindrical co-ord. how, limits are as follows volume bounded boy Z=202 and za 1.4 cm 14 mm oso sat o <r <0.5cm

So, volume ат Vp rodo drdz 72 of paraboloid, jos pat *d® dr d2 gylindrical co-ord, volume element Up = f do jo. 914 RT 0.5 dz roda po 2 27 s so (1.4-202) do o - 1 - /* (1.4 miles - + [**],"s) QT Olt ( 12 / 2 cma. 64 1.001 em 3 Vp 51 160 I cm 3 Answer) volume of para e of para boloid,

i Ve T2²h volume of cylinder, go= radius of cylinder h = height of sylinder 20.5 cm h 12 mm I.2 cm vol. of cylindrical part, Ve = t x (1.23% x0.5 cm3 18 25 Tcmo = 2.2619 cm3 so, total volume of bulled- va vo the V=G => v 18 25 71 :) cm3 160 831 8.00 3 π cm

from de finition, mass mapy where p = density of the object 11.3 glans Lere, 831 t) gm m = (4t. 3x m = 36.8756 g → = щ 36.8 76 69 Answer v mass of butter