Question

a piece of cardboard measuring 13 inches by 8 inches is formed into an open-top box by cutting squares with side length from each corner and folding up the sides. find a formula for the volume of the box in terms of

Answer 1

The volume of the box can be calculated by finding the volume of the rectangular base and multiplying it by the height. The formula for the volume of the box in terms of 'x' is: V = (13 - 2x)(8 - 2x)(x) cubic inches.

Step-by-step explanation:

The volume of the open-top box can be calculated by finding the volume of the rectangular base and multiplying it by the height. Since squares are cut from each corner, the resulting base dimensions will be reduced by twice the length of the side of the square cut.

Let's assume that the side length of the square cut is 'x'. The new dimensions of the base will be (13 - 2x) inches by (8 - 2x) inches. The height of the box will be 'x' inches.

Therefore, the formula for the volume of the box in terms of 'x' is: V = (13 - 2x)(8 - 2x)(x) cubic inches.