Question

Determine the volumes in mm of the solids generated by revolving triangular plate ABC (shown) one revolution about the following axes. 250 mm C 300 mm В 200 mm 750 mm (a) the x-axis mm3 (b) the y-axis mm -/25 Points) DETAILS NORENGSTATICS1 7.P.055. Determine the surface area in in and the volume in in or the body of revolution obtained by revolving the blue square one revolution about the a-a-axis. 76" 2.2 in A= in 2

Answer 1

Sos. Given c 2 so mm Z SOM SOO 2 300 yi coolcolate A, A₂,A3, A4 B A, a 750 x 500 = 375 000. 1200 200 !*750 x 200': 75000 Ae x A's 750 mm = 62500 X 500 X250 A3 2. Au = 1ę x 500 x 300 = 75000 A : A, -A, -A3-Au =) A = 162 500 Now calcolate 500 2 25o 750 = 375 I, 750 2 11 - 200 3 66 67 11 Y₂ x 750 = 500 2x 500 333.34 Y3 - 3 83.34 13 25 3 Ķx 300 = 400 Yu = 200 + x ५ = 250+ ſx250 = 416.67 الي 80 Y, +4,+83-84 x = x, +2, +%- Xy 2 SO 120 Ž = 541.67. The x-axis & y axis. 3 Now calcolate Ux = 255 254 403.1 mm Vac 16 2 500 x 2x x 250 =) vy - 162 500 x 2 x 1 x 541.675) Vy5530 54610.1 mm3

Х Sof' A = 1.1 inch √1. 1²+1.12 768 TH OB is ten distance of centroid 'o' Prom -a = 45 +14 LBAO = 59° 2.2in → then, sin 59 - OB OA so Til va x sin 59' OB = 1.334 =n 8.8 in ux 2.2 Square → perimeter of 4.84 in? 2.2 * 2.2 = → Area revolved Volume = Pxeln. surface area of pot) A = 8. 8x 2x it x 1.334 A: 73.75 in volume of revolution = = Asx 2 in = 4.84 x 2x ot x1.334 V = 40.56 in 3