Question

Determine the volumes in mm of the solids generated by revolving triangular plate ABC (shown) one revolution about the following axes. 250 mm С 300 mm 200 mm 750 mm (a) the x-axis 3 mm (b) the y-axis mm3

Answer 1

Let us take When revolved an element of thickness around x-axis will da form a disc • Volume of that disc Area x thickness : a(y-y2) x da (280, 6oo) Y2t Anda (250,200) B Y, A. 750 for that the equations purpose We have to find AB, AC, CB.. of lines line AB 200 a ya 750 4 15 line AL= y = 500 n 250 Ay=20 line (B ) y - 500 500-200 X - 250 250-780. y = 3a + 650 S CSScanned with CamScanner

250 2 volume falan da 0 Samsung sfl-3a + cre)* - (03.j?] + da 250 780 250 12.3367 (31. n ( - 34 (-35) -324650 S . 165 123 22513 3 280 6.425x10 + 17,386 X 10 x 107 3 Vy 8 2.3811 x 10 mm CSScanned with CamScanner

Similarly when Surface is revolved around Y-axis. We have to take a horizontal strip of thickness dy under consideration ay When this strip is f(250, 500) revolved around Y-axis it will form a disc of thickness dy X2 dy 425, 2009 .- Volume of this disc Area x thickness. A -T(-x) dy to weite equations of line in terms We have to write 15 y 4 .: Equation of AB = Equation Equation of CB AC = Ч 2 3250 - 5 -5n 3 ,'. 200 500 Volume Sal (98-09)"] day + fa [139-saj - Googde 200 1.1565 810 x108 + 2.2451 X108 & 3 Ny = 3.4016 X10 mm Scanned with CamScanner