Question

(b) Cari luas elips yang memotong satah 2x + 3y + 62 = 60 oleh silider bulat (seperti yang ditunjukkan dalam Gambarajah 1) x2 = y2 = 2x (Petunjuk: guna luas kamiran permukaan) Find the area of the ellipse cut on the plane 2x + 3y + 6z = 60 by the circular cylinder (as shown in Figure 1) x2 = y2 = 2x (Hint: use area of surface integral) Silinder bulat dengan r=1 berpusat di (1,0). Luas satu bulatan ialah TT h Circular cylinder with 1 with centered at (1,0). Area of a unit circle is TT Gambarajah 1 Figure 1 (5 markah/marks)

Answer 1

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   Summary if we have a given surface of the form. 2= 0 Z (x, y). the sw face integral Sf Flogy, zrds ffrey, 2) fit (02)²+(022 tedy where D is the projection of post s onto ky plane. * * When we have to calculate the area then we assume, flix, y, z) = solution: Now we have to find area of the of the elipse cut on the Diane 2x+3y + 6 2 = 60 By the circular pot the cylinder x² + y² = 2x or we have given that the su face. plane 2x + 3y +62 = 60 is on h SU sujace satisfies the 2x + 3y +62-60 2 Now By surface integral
   
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   so the D C projection of surface on x-y plane) classmate (21-12 + y²=1 circle with center Ciso Page will be redius rat Co didy SHOWS the area of D- & (20) 1 = m circle with TT (1)2 area of 1 radius SO faxdy > π D By Husing ea în 6 ID fs fixy, 2) ds F 6 S on the plane 2x+ 3y + 62 = 60 = 22 is So the area of the elipto aut circular cylinder x² + y² 7 $s $4274,27ds2 IT 6 By the Answer answer S 4 3.665 square zenit Answer