An open box is made from a square piece of material 24 inches on a side by cutting equal squares from the corners and turning up the sides. Write the Volume V of the box as a function of x. Recall that Volume is the product of length, width, and height.
Thank you!
let each side of the cut-out square be x in
then isn't the base 24-2x by 24-2x ?
and isn't the height of the box x ?
take it from there.
V(x)= x(24-x)^2 ?
Or V=1/3(24-2x)^2*x
I'm confused as to how you came up with the base as 24-2x.
Thanks for your help!
draw a square with sides 24 in
draw small square cut-outs at each of the corners, each of those sides is x inches long.
Now didn't you take away x inches from each end??
so 24 - x -x or 24-2x
How did you come up with that equation ??
Your equation of V(x)= x(24-x)^2
in your first response should have been
V(x)= x(24-2x)^2 ?
Okay, I just forgot the 2. Thank you so much for your help! Have a nice day!
To find the volume of the box as a function of x, we first need to determine the dimensions of the box.
When we cut equal squares from the corners of the square material, we create flaps that will be folded up to form the sides of the box. The length of each flap along the sides will be x inches since we are cutting identical squares from each corner.
Now, when we fold up the flaps, the length and width of the resulting box will be equal to the original side length of the material minus twice the length of the flaps (2x). Thus, the length (L) and width (W) of the box will be:
L = 24 - 2x
W = 24 - 2x
The height (H) of the box will be equal to the length of the flaps we folded up, which is x inches.
Therefore, the volume (V) of the box can be calculated as the product of length, width, and height:
V = L * W * H
= (24 - 2x) * (24 - 2x) * x
Thus, the volume V of the box as a function of x is V(x) = (24 - 2x)^2 * x.