Question

(calc!) A company that makes gifts and souvenirs needs to create a pyramid that has a square base and has a fixed volume of 72 cubic inches. what should the pyramids dimensions be to minimize the amount of materials needed to construct itvolume of pyramids = v = 1/3 b^2ssurface area of pyramids = s = 2bs + b^2

Answer 1

Substitute V = 72 into the volume formula:

`\begin{gathered} (1)/(3)b^2s=72 \\ \text{ Isolate the variable }s: \\ s=(72*3)/(b^2) \\ s=(216)/(b^2)---(1) \end{gathered}`

Substitute equation 1 into the Surface area formula:

`\begin{gathered} S=2b((216)/(b^2))+b^2 \\ S=(432)/(b)+b^2 \end{gathered}`

Draw the graph of the function S:

Notice that the S is minimized at b = 6.

Substitute b = 6 into equation 1:

`\begin{gathered} s=(216)/(6^2)=(216)/(36) \\ s=6 \end{gathered}`

Therefore, the correct answer is choice C:

b = 6 in. and s = 6 in.