Q28 of 39 Page 1

A metal box with a square base and vertical sides is to contain 1024 cm3. The material for the top and bottom costs ` 5 per cm2 and the material for the sides costs ` 2.50 per cm2. Find the least cost of the box.

Let x be the length and breadth of the box and height be y.

∴ Volume = V = x2y = 1024



Total cost of top and bottom = 2 × x2 × 5 = 10x2


Total cost of sides = 4 × xy × 2.5 = 10xy


∴ Total cost





∴ The cost of the box is minimum when x = 8 cm.


∴ Total cost = Rs. 1920


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