Question

An open box of maximum volume is to be made from a square piece of material 24 cm on a side by cutting equal squares from the corners and turning up the sides (see figure).

a. Write volume V as a function of x, the length of the corner squares.







b. What is the domain of the function?

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Answer 1

V = x(24 - x)^2 cm^3.

Domain = (0, 24).

Explanation:

a. Let the lengths of the sides of the squares be x cm.

Then the lengths of the sides of the base of the box will be (24 - 2x) cm.

The height of the box will be x cm.

So the required volume

= height * area of base

So V = x(24 - x)^2

b. The domain of this function is (0, 24).