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Iha
17 Sep 2017
Attempt any 4 sub parts of the following case-based question. Each sub part carries 1 mark.  

An open cylinder is to be constructed from a metal sheet so as to hold a given quantity of liquid. Let V and S denote the volume and total surface area of the open cylinder respectively. Based on the information answer the following questions from (i) to (v).

(i) The surface area (S) of the cylinder thus formed expressed as a function of 'r' as

     a) S = 2Vr + πr2      b) S = V -  πr2      c) S = 2Vr2 + πr      d) S = 2Vr + πr3

(ii) A point c in the domain of S(r) at which either S′(c) = 0 or S(r) is not differentiable is called:
     a) A critical point of S(r)      b) An inflation of S(r)      c) An inflexion point      d) A saddle point

(iii) If f'(c) = 0 and f''(c) > 0  then there is a .........

      a) local minimum at point c.
      b) local maximum at point c.
      c) saddle point at point c.
      d) critical point at point c.

(iv) For what value of 'r', the surface area of the cylinder is least.

      a) r = Vπ23      b) r = 2Vπ3      c) r = V2π13      d) r = Vπ13

(v) The cost of material will be the least 

     a) When the radius of the cylinder is twice its height.
     b) When the height of the cylinder is twice its radius.
     c) When the height of the cylinder is thrice its radius.
     d) When the height of the cylinder is equal to its radius.
 

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Cm Rate Change Surface Area Radius 2 Cm Harish Rs 429 56 Account End June Month July Deposited Rs 255 Rs 736 34 First Second Weeks RespectivTick Correct Answer Abc Ab Ac Ad Bc Ac Cf Ab Abc Symmetrical Ad B C Cf NoneAbc 65 B 45 Find C FigureMark Correct Answer Given Figure Pq Rs Pab 60 Acs 100 Bac 40 B 60 C 80 50 Parallelogram Abcd Ab 18 Cm Bc 12 Cm Al Dc Bc Al 6 4 Cm Find Length Saree 5 Long 1 3 Wide Border Width 25 Cm Printed Along Sides Find Cost Printing Border Rs 1 Per 10 CFunction F X Defined F X X2 7x 4 F 7 X 4 42 Approximate Value X List Main Functions District Administration Volume Spherical Balloon Increasing Rate 25 Cm3 Sec Find Rate Change Surface Area Instant Radius 5 CShow Maximum Volume Cylinder Inscribed Sphere Radius Cm 500 Cm3 Total Cost C X Associated Production Making X Units Item Given C X 0 005 X3 0 02 X2 30 X 5000 Find ASurface Area Spherical Bubble Increasing Rate 2 Cm2 Sec Find Rate Volume Bubble Increasing Instant RFind Point Curve Y2 4x Nearest Point 2 8 Prove 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Min Away Lamp Post 6 High Rate Length Shadow IncreasesUse Following Information Answer Next Question Ladder 13 Long Leaning Wall Bottom Ladder Pulled AlonLength Rectangle Decreasing Rate 3 Cm Width H Increasing Rate 3 Cm 8 Cm B 6 Cm Rate Change PerimeterUse Following Information Answer Next Question Sand Pouring Pipe Rate 15 Cm3 Falling Sand Forms ConeSurface Area Spherical Bubble Increasing Rate 4 Cm2 Radius Bubble 8 Cm Rate Volume Bubble IncreasingSide Square Sheet Increasing Rate 6 Cm Min Rate Area Increasing Side 12 Cm Long Use Following Information Answer Next Question Kites First Seen 3 000 Years Ago China Became PopularRelation Time Distance Given Equation My2 Ny N Constants Velocity Time GivenVelocity Particle Moving Straight Line Given V2 Xex GivenLaw Motion Particle Moving Straight Line Given EqualRate Change Volume Sphere Respect Surface Area Radius 12 Cm Use Following Information Answer Next Question Archery Competition Organized Sheriff Nottingham RobiVolume Sphere 352 Cm3 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