Question

1) A rectangular storage container with an open top is to have a volume of 15 m 3 . The length of its base is four times the width. [2pts] a. Write an equation for the volume of the container in terms of the height (h) and the width (w). [3pts] b. Write an equation for the surface area of the container in terms of w and h. [2pts] c. Re-write the equation from part (b) so that it gives the surface area in terms of w only. [3 pts] d. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Write an equation for the cost of the materials for the container.

Answer 1

9514 1404 393

Answer:

a) V = 4w²h

b) SA = 4w² +10wh

c) SA = 4w² +37.5/w

d) C = 40w² +225/w

Explanation:

The relevant formulas are ...

V = LWH

base area = LW

lateral area = H(2(L+W))

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a) The length is 4 times the width, so the volume is ...

V = (4w)(w)(h)

V = 4w²h

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b) The total surface area is the sum of the base area and the lateral area:

SA = base area + lateral area

SA = (4w)(w) + 2h(4w +w)

SA = 4w² +10wh

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c) The volume is 15 m³, so the height in meters in terms of the width in meters is ...

15 = 4w²h

h = 15/(4w²)

Then the surface area is ...

SA = 4w² +10w(15/(4w²))

SA = 4w² +37.5/w

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d) The equation we have for surface area has one term for base area and a second term for lateral area. We can apply the cost factors to those terms to get the cost of materials:

C = 10(4w²) +6(37.5/w)

C = 40w² +225/w