You are hired to help minimize production costs. Your job is to choose the form of packaging for a new product from the five choices below. The package must hold at least 1000 cubic inches. The cost of the cardboard for the packaging is $0.03 per square inch.

Your project should include the volume, total surface area, and materials cost for each solid given below, including the formulas you used and each step of your work. Make sure to use the formulas given in your lessons and round your answers to the nearest hundredth.

Question

You are hired to help minimize production costs.  Your job is to choose the form of packaging for a new product from the five choices below.  The package must hold at least 1000 cubic inches.  The cost of the cardboard for the packaging is $0.03 per square inch.  

Your project should include the volume, total surface area, and materials cost for each solid given below, including the formulas you used and each step of your work.  Make sure to use the formulas given in your lessons and round your answers to the nearest hundredth.

anonymous · Answer

Also, this goes along with it. :)

Solid 1:  Square Prism with each side of the base equal to 10 in. and a height of 8 in.



Solid 2:  Square Pyramid with each side of the base equal to 13 in. and a height of 21 in.



Solid 3:  Cylinder with a radius of 7 in. and a height of 8 in.



Solid 4:  Cone with a radius of 10 in. and a height of 9 in.



Solid 5:  Sphere with a radius of 7 in.

janu16 · Answer

didnt you just post this like 30 minutes ago?

anonymous · Answer

Yes, but nobody would answer me. @Janu16

janu16 · Answer

@rebeccaxhawaii

janu16 · Answer

@jhonyy9

michele_laino · Answer

hint:
we have to choose the solid shape which has the least total surface

anonymous · Answer

Okay. I have my formulas, but I need to understand how to plug in the info into the formula. Could you help me with that?

anonymous · Answer

@Michele_Laino

michele_laino · Answer

ok!

anonymous · Answer

Thank you! :)

michele_laino · Answer

for example, if we take the sphere with a radius of 7 meters, we have this volume:
$$V = \frac{{4\pi }}{3}{r^3} = \frac{{4 \times 3.14}}{3} \times {7^3} = 1436{m^3}$$

michele_laino · Answer

and the total Surface, is:
$$S = 4\pi {r^2} = 4 \times 3.14 \times {7^2} = 615.44{m^2}$$

anonymous · Answer

That's easy to understand so far.

michele_laino · Answer

so, please take a note of that surface

anonymous · Answer

Okay.

michele_laino · Answer

next let's consider the solid 4), namely the cone

anonymous · Answer

Okay

anonymous · Answer

When I do these, am I just doing the total surface area or do I need to include the lateral as well?

michele_laino · Answer

here the volume is:
$${V_4} = \frac{{\pi {r^2}h}}{3} = \frac{{3.14 \times {{10}^2} \times 9}}{3} = ...inche{s^3}$$

michele_laino · Answer

I think that we have to compute the total Surface, since we have to mi nimize the cost of cardboard for packaging

anonymous · Answer

Okay

michele_laino · Answer

please complete

michele_laino · Answer

what is $V_4$?

anonymous · Answer

210.6?

anonymous · Answer

or would it be 842.4?

michele_laino · Answer

I got $V_4=942$

anonymous · Answer

Okay, that's probably the correct answer.. I didn't round like it stated, I'm sorry lol

michele_laino · Answer

ok! Next we have to compute the total Surface of such cone

anonymous · Answer

Okay! :) also, thank you so much for helping. This means so much!

michele_laino · Answer

the total Surface $S_4$ of such cone, is:
$$\begin{gathered}
  {S_4} = \pi {r^2} + \frac{{2\pi r\sqrt {{r^2} + {h^2}} }}{2} =  \hfill \
   \hfill \
   = 3.14 \times {10^2} + \frac{{2 \times 3.14 \times 10 \times \sqrt {{{10}^2} + {9^2}} }}{2} = ...? \hfill \ 
\end{gathered} $$

anonymous · Answer

This is probably wrong, but I got 3171.4... Ha....

michele_laino · Answer

more explanation:
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