Question

A box of cereal measures 8 in. wide, 11 in. high, and 2 in. deep. If all surfaces are made of cardboard and the total amount of overlapping cardboard in the box is 7 in. squared, how much cardboard is used to make the cereal box?

Answer 1

Total area of cardboard used will be `259` square inches.

Explanation:

We can stand the box on its base, whose area will match the top of the box, and these will be the two smallest surface areas so we will start with the smallest given dimensions of `2iDxx8iW`.

Then: `A_(t,b)=2(DxxW)`

Where `A_t,b` is the areas of both the top and base (`2xxA`);

`A_(t,b)=2(2ixx8i)=32i^2`

Then we need to move to the two sides, which will have the next largest dimensions:

Where `A_l,r` is the areas of both the LHS and RHS (`2xxA`);

`A_(l,r)=2(2ixx11i)=44i^2`

Then we need to move to the front and back faces, which will have the largest dimensions:

Where `A_f,b` is the areas of both the front and back (`2xxA`);

`A_(f,b)=2(8ixx11i)=176i^2`

Then the total area required including the overlap is;

`A_t=A_f,b+A_l,r+At,b+A_o`

`= 176i^2+44i^2+32i^2+7i^2 = 259i^2`