Question

Determine the volumes in mm3 of the solids generated by revolving triangular plate ABC (shown) one revolution about the following axes. 105 mm 126 mm B 84 mm A 315 mm (a) the x-axis mm 3 (b) the y-axis mm3

Answer 1

Sof: Given 210 - y, los mm 105mm 2 1126 mm coolcolate ,,Agi Au Az i Al 315 x 210 = 66 150 84 mm Az 1 2 x 315x8u = 13230 11025 315MM A3 1/2 x 210 x 10 5 = = 13230 Au = le x 210 x126 Az - Au =) A = 28665 A = A, A₂ Now calcolate 210 los 1 2 xi 315 2 = 137.5 84 28 2x315 210 Tz 3 1 x2 11 3 140 2x210 83 35 11 los 33 8 168. 84 + 2x126 3 175 Уч - axlos 3 cu 105 + Now lo Y,+Y₂ + Y3 - Yq X = X, + xy + x3 - Xy 100 105. 2 27.5

Now coolcolate the x-axis. Vac 18911 288.22 = Voc 28665 X 2 X M X 105 vy vy 2866 5 x ex ot x 227.5 - 140974457.8