Question

please help with one question :) Design a new cereal box that will hold the same amount of cereal but reduce manufacturing costs. Prove that your new design holds the same amount but can be manufactured more cheaply.
The original box was a rectangular prism and had the surface area of 290inches^2 and a volume of 264in^2

the new box needs to be with the cube formulas.. I know that the surface area is supposed to be less and the volume is supposed to be the same between the two. someone please help me solve this?

Answer 1

now.. notice the picture below

it has a front-and-back of 11x4
it has a left-and-right of 6x4
and a top-and-bottom of 6x11

now, if the Surface Area is less than 290in², then is cheaper to manufacture, because it uses less material to make the box

Answer 2

Answer:

Step-by-step explanation:

New cereal box is in the form of a cube.

So from the formula of volume of cube a a³

Where a is the side of the cube.

This volume is equal to the volume of the original box

a³ = 264 inch³

a = 6.415 inch

Now the surface area of the box will be

S = 6a²

S = 6 × (6.415)² = 246.91 inch²

Which is less than the surface area of the original box.

Therefore, manufacturing cost of the new cereal box will be less.