An artist creates models of square pyramids. For each pyramid created, the height is 2 times the side length of the base, s. The cost of eac

An artist creates models of square pyramids. For each pyramid created, the height is 2 times the side length of the base, s. The cost of each pyramid is based on volume and is $0.30 per cubic centimeter.

The cost, C(s), in dollars of a pyramid with base side length, s, is given with the following function. 

Which statement best describes the coefficient of s³?

• the product of the ratio of the height to the side length and the price per cubic centimeter
  
•  

  the product of the ratio of the height to the base area, one-third, and the price per cubic centimeter
  
•  

  the product of the ratio of the height to the side length, one-third, and the price per cubic centimeter
  
•  

  the product of the ratio of the height to the base area and the price per cubic centimeter

   

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  The volume of a square pyramid in our example is  given by  V = (1/3)(s ²)(h)   Where s is the side length of the base (thus s ² is the area of the base) and h is the height.  In our example the height is twice the side length so we would have  V = (1/3)(s ²)(2s). And to get the total cost, we would multiply this volume by (.30). So we would have (1/3)(2)(.30)s ³ = (1/3)(2)(30/100)s ³ = (2/3)(30/100)s ³ = (20/100)s ³ = 0.2s ³ and the coefficient would be equal to the product of the ratio of the height to the side length (2), times one-third, times the cost per cubic centimeter (.30 or 30/100).

   

  Thus, the third choice is the correct one.

   

        

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