Polynomials Volume

SHOW ALL WORK A metal worker wants to make an open top box out of a sheet of metal by cutting equal squares from each corner. The sheet of metal is a 10 inch by 14 inch rectangle. Using your dimensions from the previous question, write a function in standard form in terms of x to represent the volume of the box.

SHOW ALL WORK

Using your calculator or Desmos, determine the dimensions that will maximize the volume of the box. Round to two decimal places.

Hint: plug in x-value of max!

Given the open top box, what is the maximized volume of the box?

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A 16cm x 30cm sheet of rectangular cardboard is folded such that an open topic box is created. What are the dimensions that maximize the volume?

• 16cm x 30cm x 0cm

• 23cm x 9cm x 3 cm

• 8cm x 15cm x 4cm

• 23.3cm x 9.3cm x 3.3cm

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A box is created from a square piece of cardboard by cutting a square from each corner and then folding up the sides.

What would be the total volume, in standard form, that the pictured cardboard could hold?

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open topic box is created. What is the maximized the volume?

A 16cm x 30cm sheet of rectangular cardboard is folded such that an open topic box is created. What is the volume equation that models all of the boxes that can be from the piece of cardboard? Choose all that apply.

Find the volume of the rectangular prism with length (x + 2), width (x - 4), and height (2x + 1).

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