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Free_Kalibri [48]
3 years ago
9

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

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?
Mathematics
1 answer:
galben [10]3 years ago
4 0

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

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