Question

mensuration : calculation of position of center of volume for common solids

Answer 1

Ya wuction : Calculation of position of enter of volume for commen solids solution; o centre of volume of Uniform Solid Cylinder G T het take a elemental disc at depth ly from verter O. du m ed H. of midth 'dy. Its radius is 'R of may Udr. Mais of disc dm : M av Em Xara dy dite teamvalamily) A V V in der=MTA (82) dy sdm=May 184 dm = mye dy o n H we know that Je Claude of vol.) = in sang-an day xg - Hospedy yer to the 2] - [t] so, Centre of volume of Uniform Cylinder is located at I below its vester o. (5) Centre of volume of Uniform solid cone 154 A T het take a elemental disc at depth i from verten o of width idy' of mais dem. It radius is 'n Mors of disc den-Mav Here y-R MER dem=3m m x R4 dy TRT e t Trzdy i salg (due to similarity) der=3M ge dy 0 we can take of vol.) - Insomy: 3 ye dy xy = 33 Sydy 3 [1] - D or] =3 27-37 So, Centre of volume of solid cone 15 34 from verty + H from base iii) Centre of volume of Salid Hemiskt het consider elemental disc of mais din 4 radius r . Mays of disc dm = m Here ERE RE22+ y2 dir= 3M 2M (R=45) dy – :.8= VREY2 So, yen samy - 53m (R=y") dy ry - R3 "L(Ry - y3) df = R-*76 of width dy 4 RM so, cenk of volume of solid Henisphen is 35 frem base.