SOLUTION: Given a square piece of material 25 inches on each side, we are to make an open box by cutting a square with x inches on a side from each corner and turning up the sides. Express t

Question 121886: Given a square piece of material 25 inches on each side, we are to make an open box by cutting a square with x inches on a side from each corner and turning up the sides. Express the volumn V of the box in a function of x.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If you cut a square of side x from the corners of a 25 by 25 sheet, the length of each side of the bottom of the box will be 25 - 2x. The volume of a rectangular solid is , here l = 25 - 2x, w = 25 - 2x, and h = x, so:

Using FOIL:

Distribute the x and collect terms:

RELATED QUESTIONS
An open box is to be made from a square piece of material, mc001-1.jpg inches on a side,... (answered by addingup)

An open box with a square base is to be made from a square piece of cardboard 30 inches... (answered by checkley77)

3. A piece of cardboard measuring 10 inches by 15 inches is to be made into a box with... (answered by ankor@dixie-net.com)

An open box made from a square piece of cardboard 14 inches on a side by cutting... (answered by greenestamps,josgarithmetic,ikleyn)

The area of the rectangular piece of cardboard shown on the left is 198 square inches.... (answered by ankor@dixie-net.com)

The area of the rectangular piece of cardboard shown on the left is 171 square inches.... (answered by alicealc)

An open box is made from a square piece of cardboard 46 inches on a side by cutting... (answered by josgarithmetic)

An open box is made from a square piece of sheet metal 19 inches on a side by cutting... (answered by stanbon)

Peter has a piece of metal 18 inches wide and 20 inches long, he wants to make an open... (answered by ankor@dixie-net.com)