Question

A supermarket employee wants to construct an open-top box from a 14 by 30 in piece of cardboard. To do this, the employee plans to cut out squares of equal size from the four corners so the four sides can be bent upwards. What size should the squares be in order to create a box with the largest possible volume? Do not type in units, only the numeric part of the answer. *

Answer 1

Answer: The side of the square will be 3 cm.

Step-by-step explanation:

When squares of equal size of side x, are cut from the four corners, we are left with the following dimensions for the cuboid box.

l= 30-2x

b = 14-2x

h= x

Hence, the volume of the cuboid will be ,

V = lbh

= (30-2x)(14-2x)x

Since this volume should be the largest possible, then differentiating volume with x should be equal to zero.

Therefore, $\frac{dV}{dx} = 0$

$\frac{dV}{dx} =-2(14-2x)x -2(30-2x)x+(30-2x)(14-2x)=0$

solving we get, x = 3, x = $\frac{35}{3}$

We can omit x = $\frac{35}{3}$ because 14 - 2x < 0 , which is not possible.

Therefore, x=3.