Question

I have a question I'm not sure about how to do. I only need help with one shape, but here's what I'm supposed to do: 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 500 cubic inches.  The cost of the cardboard for the packaging is $0.02 per square inch.  Choose the most cost efficient packaging (the packaging with the smallest materials cost).  Your project should include the volume, total surface area, and materials cost for each solid given below, including your work. 

Answer 1

The one shape I need help with is Square Pyramid with each side of the base equal to 10 in. and a height of 15 in.

Answer 2

I have this drawn correctly?

Answer 3

so you need the surface area?

Answer 4

What I'm trying to find is the volume, currently

Answer 5

volume is 1/3 * (area of the base) * h

Answer 6

Yeah but, the thing I need help with is --wait

Answer 7

Oh, sorry, I was confusing the slant height with the height

The thing I was having trouble finding was the slant height for the total area. Sorry, I got confused

Answer 8

but the volume is 500, right?

Answer 9

no problem...so you need to find the slant height?

the slant height is the hypotenuse of the triangle formed by drawing the extra line shown.
extra