The product of the areas of three adjacent faces of a rectangular box meeting at a corner equals:___________?
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Answer: C. the square of the volume of the box
Explanation
The areas of three adjacent rectangular faces meeting at a corner are lb, bh, and hl. Multiplying these three face areas together yields l squared times b squared times h squared. This product equals the square of the volume because volume is length times breadth times height. A rectangular box has dimensions length l, breadth b, and height h. Volume of a rectangular box is calculated as the product of length, breadth, and height. Adjacent faces share common edges meeting at a single corner vertex.
Spatial geometry principles help in calculating surface properties of three-dimensional objects. Packaging and manufacturing industries use volume and surface area relations extensively. Mathematical proofs of geometric identities develop spatial reasoning skills. Choosing volume of the box ignores the squared exponents resulting from face area multiplication. Choosing twice the volume is an incorrect algebraic scaling of the face dimensions. Choosing cube root of the volume reverses the required mathematical exponent operation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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