Question

A rectangular storage container with an open top and a square base has a volume of 8 cubic meters. material for the base costs $5 per square meter and material for the sides $2 per square meter. find a formula that expresses the total cost of materials as a function of the length of a side of the base.

Answer 1

C(h,w)=5w²+8(h*w)

Step-by-step explanation:

Let w be the name of the width of this storage.

Let h be the height of the storage.

Constraint: w²h=8 cubic meters.

Taking into acount that the base of this storage is a square, width=length.

Area of the base: w²

•The cost of the base is given by:

C(b)=$5*w²=

5w²

•The cost of the sides is given by:

C(s)={$2*(h*w)}*4

We multiply by 4 because there are 4 sides.

C(s)=8(h*w)

•The total cost should be given by:

C(h,w)=5w²+8(h*w)

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To verify this answer let's illustrate an example and solve it.

Let's say we have a storage with a base of 9m² (3 by 3, each side=3) and then the height of the storage is 4m.

Let's plug the values into the formula and try to find the total cost:

C(4,3)=5(3)²+8(4*3)= $141.

Area of the base was 9, 9*5= $45.

Area of the 4 sides should be 4*3*4= 48, 48*2= $96

$45+$96= $141, that's correct!