Question

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides (see the figure).

Find the values of x for which the volume is greater than 250 in3. (Round your answers to three decimal places. Enter your answer using interval notation.)

Answer 1

To find the values of x for which the volume is greater than 250 in³, we need to calculate the volume of the box first and set it greater than 250. Then, we can solve for x using algebraic techniques.

Step-by-step explanation:

To find the values of x for which the volume is greater than 250 in³, we need to calculate the volume of the box first and set it greater than 250. The volume of a rectangular box is given by V = lwh, where l represents the length, w represents the width, and h represents the height.

Given that the length and width of the cardboard are 30 in and 12 in, respectively, and equal squares of side x are cut from each corner, the length and width of the box will be reduced by 2x. The height of the box will be x.

So, the volume of the box is (30-2x)(12-2x)(x). Setting this expression greater than 250, we can solve for x using algebraic techniques.