Boxes hold various numbers of square-based prisms in a single column. The square base of each prism has a side length of 18 inches. The height of each prism, h , can be found using the function h of cap v is equal to cap v over 324 , where cap v is the volume of the prism. The total height of the box, b , can be found using the function b times h is equal to x h , where x is the number of square-based prisms in a specific box. Which function can be used to find the height of a box containing 4 square prisms, depending on the volume of the prisms?
Answer
A
b times h of cap v is equal to the fraction with numerator h and denominator 1 comma 296
B
b times h of cap v is equal to cap v over 81
C
b times h of cap v is equal to h over 81
D
b times h of cap v is equal to the fraction with numerator cap v and denominator 1 comma 296
Explanation
Each prism has height h(v) = v/324 because its square base has area 18 × 18 = 324 square inches. A box with 4 prisms stacked has height b(v) = 4h(v) = 4(v/324) = v/81. Therefore, the correct function is b(v) = v/81, choice D.
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