Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 23 ft by 13 ft. the resulting piece of cardboard is then folded into a box without a lid. find the volume of the largest box that can be formed in this way.

Step-by-step explanation:

Given that rectangle  has side length 23x13 feet.

When squares of side x are cut from all the four sides we have dimensions as

23-2x and 13-2x and height x

Volume

Use derivative test

First derivative V'(x)

Equate I derivative to 0

We get approximate value of x = 2.671, 9.329

Since width is 13 feet it cannot be 9.329

Hence x = 2.671

V"(x) = -80 <0

So maximum volume is

x = 25/2304

step-by-step explanation:

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft