An open top box is to be made by a 24 in by 24 in. by 36 in. piece of cardboard by removing a square from each corner of the box

Question

3 years ago

9

and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume?

1 answer:

galben [10] · Answer 1 · 2021-11-17T16:35:19+03:00

Answer:

X= -12 +6√10

X= 6.973

Step-by-step explanation:

Volume of the box= (36-2x)(24-2x)x

Volume of the box

=( 864 -96x -4x²)x

But 864 -96x -4x²

=216 - 24x-x²

Solving for x quadratically

X= (24+12√10)/-2

X= -12 -6√10

X= -30.97

Or

X= (24-12√10)/-2

X= -12 +6√10

X= 6.973

X will definitely be a positive number

So X= -12 +6√10

X= 6.973