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10. Find the general solution of the system : 13 Y 11. Find the general solution of the system: y'= ( ) 12. Compute the surface area of a cone of radius r and using surface integrals

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Z Ans: The surface area of a cone using surface integrals is obtained using parametric approach. Let a be the be the angle is swept out. Let k= tana. for height ch', the radius of this come will be r= ky where, Osn t h. k= tan a Parametrisation of this come a = scu; v) = <kucosu, kusinu, v) where, osus 2x & vos h х sy 1 = kucosu Tangent Vector, tu = kusinu, kvosuz Similarly, tu= <kosu, ksinu 소 곳 tux tv kusinu keosu ksinu tux tv kvoosu i t kusinu h + k²v Ê =) I tu x tull k²v ²a²ut k²3sinu Esinkut ketu Tk²v 2 + kr Jitk2 ✓ 2 4 2 V Hence, the surface area area of come will se, ha 27 Sfill tux tull da I S kvalite? dudu RAKWI+k? = h = v dv

क = 2xk dite 2 SA akh² /ltk² = k= tan a Since, akh² Jitka h North? It 2² ch h och It g2 52 a h ²+ SA: = ². The Lateral Surface Area of the cone is 2 iare 2 rath then the g the When, the cirallar base is included part of the cone base ie added to Total Surface Area = te th? t ni area the tu es = ne [Jorth2 +7