Question

(15 Q3. nts) 13" 3" X 7" → 3" 3"'2" Determine the x- and y-coordinates of the centroid of the shaded area. Show your calculations in full details.

Answer 1

Page no 101 13" 26 GA 62 14 .93 31 We will divide the given Area 1311 into 4, areas. 25 GI 14 G4 (63 34 6 . 4r 11 8 4 X- coordinate of controid. for centroid of composite area Using the formula X = { Aixi TA; A, x, + A2x2 Azaz Auay Since there is Cinestar and rectangular hole, we have subtracted it the formula Ai + A2 A3-Ay.

(fage no 2 where A = Area of Big rectangle 13 x 14 - 182 inch a = location of centroid of rectangle from Yaxis 1, 외에 13 2 6.5" Az = Area of Right angled Triangle = ** base xheight 1/2 x 8 x 14 56 inch? : A2= X2= X2= Location of Centroid of bangle. from Yazio 13 + (age) - Az = Area of Text? (base) = 13+ 3+ () Is. 67 inch semicircle hole Tx 3² = 14.137 inch? 2 X3 = Location of centroid of semicircle from faris 263 = 3 + 3 = .6inch A4 = Area of rectangular hole 2x6 = 12 inch ay Location of controid of rectangular hole from Yasis 3+3+3 + 3 + 1 13 inch 24 the equablan we get subo tituting all values in T = (182 x 6.5) + (56 x 15.67)- (14.137* 6)- (12 * 13) - 182 + 56 14:137 -12 Answer IX 8. 59 inch

(Page no Y co-ordinate of controid. Y TA:y: TAI Any + A22 A393 - A4.94 Asa A2 A3- Ay where 182 inch Y = Location of controid of Brg rectangle from X-axis 14 7" 11 9.- A2 56 inch? from X-aars Y = Location of controid of Triangle Iz = height = 16 - 4.67 inch. Ilm from X-4385 .Az = 14.137 inch? 93 - Location of controid of semicircle 4 *T 4x3 1.273 inch. 3T Yes 3x A4 = Ranch from Xaar Yu - Location of controid of rectangular hole 2+3 Sinch. Yua 2 + + Nlor

Pagenoy the equation Substituting all values in J = (182*7) + (50*4.07) - (4.137 x 1.273)-(12x5) 182 + 56 14.137 - 12 9 = 6 88 nch. Answer. Answers x-coordinate Of centroid (7) - 8.59 inch ::) Y - coordinate of certnord (7) I 6.88 inch.
In this numerical,we want to find the x and y co-ordinate of the shaded area.So we will divide the figure into 4 areas.Then we will use the formula of centroid of composite area and find the required coordinates.

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