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:

$\begin{gathered} \frac{1}{3}b^2s=72 \\ \text{ Isolate the variable }s: \\ s=\frac{72\times3}{b^2} \\ s=\frac{216}{b^2}---(1) \end{gathered}$

Substitute equation 1 into the Surface area formula:

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

Draw the graph of the function S:

Notice that the S is minimized at b = 6.

Substitute b = 6 into equation 1:

$\begin{gathered} s=\frac{216}{6^2}=\frac{216}{36} \\ s=6 \end{gathered}$

Therefore, the correct answer is choice C:

b = 6 in. and s = 6 in.