A cuboid has edges in a 1 : 2 : 3 ratio and an 88 cm2 surface area. What is its volume:_________?
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Answer: B. 48 cm3
Explanation
Expressing cuboid edges as x, two x, and three x allows forming a surface area equation. Solving the surface area formula yields an edge scaling factor x equal to two centimeters. Multiplying the actual edge lengths two, four, and six gives a total volume of forty eight cubic centimeters. Total surface area of a rectangular cuboid equals two times the sum of all adjacent face products. Volume of a cuboid is calculated by multiplying its length, breadth, and height dimensions together. Ratio scaling allows determining actual physical dimensions from proportional edge relationships.
Packaging designers calculate cuboid volumes to optimize shipping container space and material usage. Manufacturing rectangular containers requires balancing surface area material costs with internal storage capacity. Geometric scaling principles are widely used in engineering design and industrial fabrication. Option A suggests twenty four cubic centimeters which underestimates the calculated product of the edges. Option C suggests sixty four cubic centimeters which overstates the volume derived from the scale factor. Option D suggests one hundred twenty cubic centimeters which violates the surface area constraint.
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- Mathematics
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- Mathematics
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