SOLUTION: The bottom of a box is supposed to be a rectangle with the perimeter of 36 cm. The box must be 4 cm high. what dimensions give the maximum volume?

Question 224025: The bottom of a box is supposed to be a rectangle with the perimeter of 36 cm. The box must be 4 cm high. what dimensions give the maximum volume?
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
The bottom of a box is supposed to be a rectangle with the perimeter of 36 cm. The box must be 4 cm high. what dimensions give the maximum volume?

Step 1. The maximum volume is when the rectangle is a square and let s be the side of the square.

Step 2. The perimeter P of a rectangle (or square) means adding up all four sides. So P=s+s+s+s=4s since all four sides of the square are equal.

Step 3. But P=36=4s. Solving for s=36/4=9 cm.

Step 4. Volume V=A*h of the box where A is the area of the square and h is the height given as h=4.

Step 5. Area for a square. So square centimeters.

Step 6. Then V=A*h=81*4=324 cubic centimeters.

Step 7. ANSWER: The maximum volume of the box is 324 cubic centimeters.

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for
Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

http://www.FreedomUniversity.TV

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