Q. 235.0( 1 Vote )

Find the volume o

Answer :


Let a right circular cylinder of radius “R” and height “H” is inscribed in the sphere of given radius “r”.



Let V be the volume of the cylinder.


Then, V = πR2H


…. (1)



Differentiating both sides w.r.t H to get,


….. (2)


For maximum value put dV/dH = 0





Again, differentiating w.r.t H we get,



At ,



So, volume is maximum when height of cylinder is .


Substitute in (1) to get,





OR


Let the length and breadth of the tank are L and B.


V = 8


2LB = 8


…. (1)


Total surface area S = Area of base + Area of 4 walls


= LB + 2(B+L).2


= LB+4B+4L


The cost of constructing the tank is:


C = 70(LB) + 45(4B + 4L)



….. (2)


Differentiating both sides w.r.t L we get,


…. (3)


For minimization dC/dL = 0,



L2 = 4


L = 2


Differentiate (3) w.r.t L to get,



Cost is minimum when L = 2.


From (1),


B = 2


From (2),



= 280 + 720


= Rs 1000


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