Question

A manufacturer wants to double the volume of a 12 in.× 3 in.× 7 in. box, while using as little extra cardboard as possible. Which statement is true?

1) The manufacturer needs to add 12 in. of extra cardboard
2) The manufacturer needs to add 21 in. of extra cardboard
3) The manufacturer needs to add 24 in. of extra cardboard
4) The manufacturer needs to add 42 in. of extra cardboard

Answer 1

To double the volume of the box, the manufacturer needs to add 42 in. of extra cardboard.

Step-by-step explanation:

To double the volume of the box while using as little extra cardboard as possible, we need to find the new dimensions of the box. The original volume is 12 in. × 3 in. × 7 in. = 252 cubic inches. To double this volume, we need to find a new set of dimensions that will equal 504 cubic inches. Let's call the length, width, and height of the new box x, y, and z respectively. We can set up the equation:

x * y * z = 504

From this equation, we can see that the manufacturer needs to add 42 in. of extra cardboard. Therefore, the correct answer is option 4) The manufacturer needs to add 42 in. of extra cardboard.