The designers of drink cartons must consider the length of the straw required so that it will reach the bottom of the carton. We will make the following assumptions:
-the straw must stick out of the carton by an additional 1.5 cm
-the hole is at one vertex of the carton
-the straw must be able to reach into the diagonally opposite corner of the base of the carton
use the formula a^2+b^2+c^2=d^2
CHECK IMAGE FOR VISUAL REPRESENTATION OF THE CARTON

The length of the straw is 13.53 cm

Step-by-step explanation:

Rectangular Prism

A rectangular prism or cuboid is a box-shaped object. It has six flat faces and all angles are right angles. And all of its faces are rectangles.

If the straw must reach into the diagonally opposite corners of the base of the carton, then its minimum length is calculated by:

Where a,b, and c are the dimensions of the cuboid. The image shows the dimensions of the drink carton: a=6 cm, b=10 cm, c=4 cm (order is not important), thus:

d= 12.33 cm

The straw must stick out of the carton by an additional 1.5 cm, thus the total length of the straw is: 12.33 + 1.5 = 13.53 cm