A rectangular storage container with an open top has a volume of 20 3 . The length of its base is twice its width. Material for the base costs $20 per square meter; material for the sides costs $8 per square meter. Express the cost of materials as a function of the width of the base.

Correct question is;

A rectangular storage container with an open top has a volume of 20 m³. The length of its base is twice its width. Material for the base costs $20 per square meter; material for the sides costs $8 per square meter. Express the cost of materials as a function of the width of the base.

C = 40W² + 480/W

Step-by-step explanation:

We are given;

Volume; V = 20 m³

Length of base is L

Width of base is W

We are told L = 2W

Formula for volume of a cuboid = LWH

Thus;

20 = 2W × W × H

20 = 2W²H

H = 10/W²

Now, we are given cost of materials for base and sides.

Formula for base area = LW = 2W²

Formula for side areas = 2(LH) + 2(WH) = 2(2WH) + 2WH = 6WH = 6W(10/W²) = 60/W

Cost per Sq.m of base = $20.

Thus, base cost = 20(2W²) = 40W²

Cost per Sq.m of sides = 8(60/W)

Thus,sides cost = 480/W

Total cost of sides and base is;

C = 40W² + 480/W

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step-by-step explanation:

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