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A company shipped a package with 4 identical spherical glass ornaments inside a box that is 8 inches long, 8 inches wide, and 4 inches tall. The diameter of each ornament is 3 inches.

The ornaments were protected by packing material that filled the box around the ornaments. The packing material coste $0.02 per euble inch,
Approximately how much did the packing material cost the company?

A. $4.84
B. $3.99
C. $5.19
D. $2.86

User Uesp
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1 Answer

5 votes

Final answer:

The cost of the packing material for the company is approximately $5.19.The cost of packing material for ornaments is approximately $5.19, considering volume, cost per cubic inch, and calculations.Option C is the correct answer.

Step-by-step explanation:

The volume of each spherical ornament is given by the formula V = (4/3)πr^3, where r is the radius of the ornament. The diameter of each ornament is 3 inches, so the radius is 1.5 inches. Substituting this value into the formula, we get V = (4/3)π(1.5^3) = (4/3)π(3.375) = 14.125π cubic inches.

The volume of the box is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the box. Substituting the given values, we have V = 8*8*4 = 256 cubic inches.

The volume of the packing material can be found by subtracting the combined volume of the ornaments from the volume of the box: V_packing = V_box - 4V_ornament = 256 - 4(14.125π) = 256 - 56.5π cubic inches.

The cost of the packing material is given as $0.02 per cubic inch. Multiplying the volume of the packing material by the cost per cubic inch, we get the total cost of the packing material: Cost = V_packing * $0.02 = (256 - 56.5π) * $0.02 ≈ $5.19.

User Chris Wagner
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