DarcFox11
contestada

Please Help! I need this by today! 15 points!
Volume and surface area are often compared by manufacturers in order to maximize how much of something can go inside of a package (volume) while keeping how much material is required to create the package (surface area) low. Pick a product that might be packaged in the shape of a rectangular prism. A rectangular prism has three dimensions: length, width, and height. The surface area of a rectangular prism can be found using the formula SA = 2lw + 2wh + 2lh. The volume of a rectangular prism can be found using the formula V = lwh. Write an expression for the ratio of surface area to volume for the figure. 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?

Respuesta :

Edufirst
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