Question

a box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. the graph below shows how the volume of the box in cubic inches, v, is related to the length of the side of the square cut - out in inches, x.

a. the point (0.25,24.438) is on the graph. this means that when the volume of the box is

cubic inches, the cut - out length is

inch(es).

b. when the cut - out length is 3 inches, the volume of the box is 54 cubic inches. this means that the point

is on the graph above.

c. suppose the largest possible cut - out length is 4.5 inches. over what interval of x does the volume of the box decrease as the cut - out length gets larger? (enter your answer as an interval.)

Explanation:

Step1: Interpret point (0.25, 24.438)

The first - coordinate is cutout length, second is volume.

Step2: Form point from given cutout and volume

Given cutout length $x = 3$ and volume $V=54$, the point is $(3,54)$.

Step3: Identify decreasing interval

From the graph, volume decreases for $x$ values from the maximum - volume point ($x = 1.7$) to the largest possible cutout length ($x = 4.5$). So the interval is $[1.7,4.5]$.

Answer:

a. 24.438; 0.25
b. (3, 54)
c. [1.7, 4.5]