4 An open top box with a square base of length z and height

4. An open top box with a square base of length z and height y is to be constructed so that its volume is 3160 cm3. The cost of the materials for the box is S0.10 per square centimeter. Find an expression for the cost of the box C as a function of the length of the base x. ( (x) ; o.ly?31 A. C(x)= 0.12+1264 B. C(x) = 0.1x3 (C) C(x) = 0.1x2 + D. C(x)= 0.6x3 E. C(x) = 0.2x2 + 316 316

Solution

volume of box ,V=x*x*y

V=x²y

given volume,V=3160

=>x²y=3160

=>y=3160_/x²

survace area of open top box ,S=x²+4xy

total cost of box,C(x,y) =0.10*S

total cost of box,C(x,y) =0.10*(x²+4xy)

total cost of box,C(x,y) =0.10*(x²+4x*(3160_/x²))

total cost of box,C(x) =0.10*(x²+(12640_/x))

total cost of box,C(x) =0.1x²+(1264_/x)