By cutting away an x-by-x square from each corner of a rectangular piece of cardboard and folding up the resulting flaps, a box with no top can be constructed. If the cardboard is 12 inches long by 12 inches wide, determine the value of x that yields the maximum volume of the resulting box. x = 2 inches Use this value of x to compute the maximum volume of the box. Maximum volume of box = cubic inches
Added by G F.
Close
Step 1
Step 1: The volume of the box is given by \( V = (12-2x)(12-2x)x \). Show more…
Show all steps
Your feedback will help us improve your experience
Vishal Parmar and 57 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
By cutting away an x-by-x square from each corner of a rectangular piece of cardboard and folding up the resulting flaps, a box with no top can be constructed. If the cardboard is 12 inches long by 12 inches wide, find the value of x that will yield the maximum volume of the resulting box.
Darshan M.
A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 4 inches by 8 inches. Six squares will be cut from the cardboard: one square will be cut from each of the corners, and one square will be cut from the middle of each of the 8-inch sides. The remaining cardboard will be folded to form the box and its lid. Letting x represent the side-lengths (in inches) of the squares, use the graphing calculator to find the value of x that maximizes the volume enclosed by this box. Then give the maximum volume. Round your responses to two decimal places.
Supreeta N.
Jason H.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD