To determine the cost of the boxes with given base areas, we'll first calculate their volumes and then use the price per cubic inch to find the costs.
Volume CalculationThe volume of a cuboid is given by:
Volume=Length×Width×Height
Since the length and height are given as 6 inches and 9 inches respectively, we can use the base area to find the width.
For the box with a base area of 24.5 square inches:Base Area=Length×Width
24.5=6×Width
Width= 24.5/6 ≈
4.0833 inchesNow, calculate the volume:
Volume=6×4.0833×9
Volume=220.5 cubic inchesFor the box with a base area of 32.75 square inches:Base Area=Length×Width
32.75=6×Width
Width= 32.75/6 ≈
5.4583 inchesNow, calculate the volume:
Volume=6×5.4583×9
Volume=295.5 cubic inchesCost CalculationThe cost per cubic inch is $2. Hence, the cost of each box is given by:
Cost=Volume×2
Cost of the box with a base area of 24.5 square inches:Cost=220.5×2=
441Cost of the box with a base area of 32.75 square inches:Cost=295.5×2=
591Closest values in the table:
Base area 24.5 square inches: $440 (closest to $441)
Base area 32.75 square inches: $590 (closest to $591)
Therefore, the selections are:
Base area 24.5 square inches: $440
Base area 32.75 square inches: $590