A box is to be made out of a 10 cm by 14 cm piece of cardboard. Squares of side length x cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.

(a) Express the volume V of the box as a function of x.

b) Give the domain of V in interval notation. (Use the fact that length and volume must be positive.)

please help mee!! with the domain part!!

Question

A box is to be made out of a 10 cm by 14 cm piece of cardboard. Squares of side length x cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.

(a) Express the volume V of the box as a function of x.

b) Give the domain of V in interval notation. (Use the fact that length and volume must be positive.) 


please help mee!! with the domain part!!

anonymous · Answer

the answer i got was (10-2x)(14-2x)(x), i just don't get why the domain has to be positive

anonymous · Answer

Okay, so a box is cut from each corner. If you do that, you only have so much paper to cut (given your paper size) and you can only cut halfway in each direction because if you cut 10cm in one direction then there is no more paper. So, what would the domain be?

mathstudent55 · Answer

|dw:1386538818156:dw|

mathstudent55 · Answer

|dw:1386538955230:dw|

mathstudent55 · Answer

Look at 10 - 2x and 14 - 2x.
If x is 5, then 10 - 2x = 10 - 2(5) = 10 - 10 = 0.
This means x must be less than 5.

anonymous · Answer

You would also use parenthesis rather than brackets because the maximum amount you can cut should not be inclusive. Because then you wouldn't have anything to make the walls of your box!

mathstudent55 · Answer

$V = (14 - 2x)(10 - 2x)(x) $

Use x = 0 and x = 5 in the equation above and get two values for V.
Those two values are the limit of maximum and minimum volumes.
V will be between those two values.

anonymous · Answer

Thankyou so much guys! @mathstudent55 and @kylie.spencer16

mathstudent55 · Answer

You're welcome.