Question

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?

Answer 1

Product: Iphone 6s plus box
W= 3in L= 6in H= 3in
And then use the surface area equation ( SA = 2lw + 2wh + 2lh)
To get your volume use the equation ( V = lwh)
And then divide those two SA / V and you get your ratio
Task 1 complete!!

Answer 2

`Ratio=(2lw+2wh+2lh)/(lwh)`

Explanation:

`Ratio=(2lw+2wh+2lh)/(lwh)`

We have been given the formula for volume and the surface area as

SA=2lw+2wh+2lh

V= lwh

Hence the ration will be

`Ratio=(2lw+2wh+2lh)/(lwh)`

Let us apply this to a tissue box measuring

l=6 in , w=3 in , h=2 in

SA=2*6*3+2*3*2+2*2*6

SA=36+12+24=24 sq in

Volume=6*3*2=36 in cube

`Ratio=(24)/(36)`

`Ratio=(2)/(3)`