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Tatiana [17]
1 year ago
9

A rectangular storage container without a lid is to have a volume of 10 m3. the length of its base is twice the width. material

for the base costs $15 per square meter. material for the sides costs $9 per square meter. let w denote the width of the base. Find a function in the variable w giving the cost C in dollars) of constructing the box.
Mathematics
1 answer:
Valentin [98]1 year ago
3 0

The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

<h3>How to determine the function?</h3>

We have a rectangular storage container without a lid.

  • Volume, V = 10 m³
  • Length, l = 2w
  • Width, w = w
  • Base costs $15/m²
  • Sides costs $9/m²

The formula of volume of the box is

V = l × w × h

Where

  • l = length
  • w = width
  • h = height

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

Learn more about function of area here:

brainly.com/question/28698395

#SPJ4

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