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 co

Question

2 years ago

6

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 co

rners 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?

Mathematics

1 answer:

mr Goodwill [35] · Answer 1 · 2022-07-20T00:21:03+03:00

Answer:

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

Domain = (0, 24).

Step-by-step 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).