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23 Jul 2020

A toy manufacturer can produce boxes of toys at a rate of . What is the total number of boxes the company can produce in ?

Booster class
AP Calculus AB
Skill
Use accumulation functions and definite integrals in applied contexts
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1 Sep 2020

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A toy manufacturer can produce boxes of toys at a rate of . Find the total number of boxes the company can produce in .

Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners

and bending up the sides. Find the largest volume that such a box can have.

  1. Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes. Does it appear that there is a maximum volume? If so, estimate it.

  2. Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols.

  3. Write an expression for the volume.

  4. Use the given information to write an equation that relates the variables.

  5. Use part (d) to write the volume as a function of one variable.

  6. Finish solving the problem and compare the answer with your estimate in part (a).

A box has a length of 18.7 cm and a width of 19.2 cm and it is 20.3 cm tall.

(a) What is its volume?

(b) How precise is the measure of the length of volume?

(c) How tall is a stack of 12 of these boxes?

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