Question

Please Help! I need this by today! 15 points!

Answer 1

l = length

w = width

h = height


SA = 2lw + 2wh + 2lh.


V = lwh.


Write an expression for the ratio of surface area to volume:


SA / V = [ 2lw + 2wh + 2lh] / lwh 

SA / V = 2lw / lwh + 2wh / lwh + 2lh / lwh

SA / V = 2/h + 2/l + 2/w



Choose an appropriate length, width, and height for your package so that it can fit the product you are shipping. Using these dimensions, what is the ratio of surface area to volume?

I will work with an hypothetical figure where you have , l, w and the volume.


I suppose you know the volume, because it is the amount of product you need to pack. Make V = 1000 cm^3, l = 10 cm and w = 5 cm.

Wtih two dimensions and the volumen you can find the other dimension.


V = lwh = 1000 cm^3 => h = 1000 cm^3 / (lw) = 1000 cm^3 / (10 cm * 5 cm)


h = 1000 cm^3 / (50 cm^2) = 20 cm


Now you have the three dimensions to pack 1000 cm^3 of your product:

l = 10 cm
w = 5 cm
h = 20 cm


And the ratio of surface area to volume is:

SA / V = 2/h + 2/l + 2/w = 2/(20cm) + 2/(10cm) + 2/(5cm) = 0,7 (cm)^-1