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16 Jul 2024, 07:03
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Base area 24.5 square inches: $440
Base area 32.75 square inches: $590
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
79% (02:39) correct
21%
(02:47)
wrong
based on 851
sessions
History
Date
Time
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A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.
The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.
The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.
|
| Base area 24.5 square inches | Base area 32.75 square inches | |
| $293 | ||
| $367 | ||
| $440 | ||
| $515 | ||
| $590 | ||
| $663 |
ShowHide Answer
Official Answer
Base area 24.5 square inches: $440
Base area 32.75 square inches: $590
16 Jul 2024, 07:06
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Bunuel
Experts' Global Explanation:
Length = 6 inches
Breadth is unknown
Height = 9 inches
I.
Base area = 24.5 square inches
Length x Breadth = 24.5 square inches
Volume = Length x Breadth x Height = 24.5 x 9 ≈ 220 cubic inches
Cost = 2 x Volume = 2 x 220 = $440
II.
Base area = 32.75 square inches
Volume = Length x Breadth x Height = 32.75 x 9 ≈ 300 cubic inches
Cost = 2 x Volume = 2 x 300 = $600
Hence, for “Base area 24.5 square inches” column, “440”, and for “Base area 32.75 square inches” column, “590” is the correct combination of the answer choices.
16 Jul 2024, 07:59
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V= l*b*h
cost= 2*(lbh)
one box1- L*b =24.5 and h=9
CP of box1= 2*24.5*9=440(approx)
same for box2= 2* 32.75*9 = 590 (approx)
cost= 2*(lbh)
one box1- L*b =24.5 and h=9
CP of box1= 2*24.5*9=440(approx)
same for box2= 2* 32.75*9 = 590 (approx)
16 Jul 2024, 08:02
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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 Calculation
The 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 inches
Now, calculate the volume:
Volume=6×4.0833×9
Volume=220.5 cubic inches
For 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 inches
Now, calculate the volume:
Volume=6×5.4583×9
Volume=295.5 cubic inches
Cost Calculation
The 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=441
Cost of the box with a base area of 32.75 square inches:
Cost=295.5×2=591
Closest 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
Volume Calculation
The 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 inches
Now, calculate the volume:
Volume=6×4.0833×9
Volume=220.5 cubic inches
For 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 inches
Now, calculate the volume:
Volume=6×5.4583×9
Volume=295.5 cubic inches
Cost Calculation
The 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=441
Cost of the box with a base area of 32.75 square inches:
Cost=295.5×2=591
Closest 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
