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# 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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