If the lengths of all the edges of the rectangular solid in the preceding figurewere doubled, what would be the surface area, in square inches, of the new rectangular solid?

Rationale

The surface area of the new rectangular solid would be 304 square inches.

When the lengths of all the edges of a rectangular solid are doubled, the surface area increases by a factor of four. This is because surface area is proportional to the square of the dimensions of the solid. Thus, if the original surface area is known, multiplying it by four gives the surface area of the larger solid.

A (152) YOUR ANSWER

This choice represents a surface area that is too low, suggesting a miscalculation or misunderstanding of how surface area scales with linear dimensions. Doubling the dimensions should yield a much larger surface area, thus making this option incorrect.

B (160) YOUR ANSWER

This value is also insufficient, indicating that the calculation did not account for the proper scaling of the surface area. Like option A, this choice fails to reflect the fourfold increase expected from doubling the dimensions.

C (304) CORRECT

This option correctly reflects the fourfold increase in surface area resulting from doubling the dimensions of the rectangular solid. If the original surface area was 76 square inches, then doubling the edge lengths yields a new surface area of 304 square inches, confirming this as the accurate answer.

D (320) YOUR ANSWER

This answer is slightly higher than the correct value, indicating an overestimation of the surface area. It incorrectly assumes a different scaling factor rather than the correct fourfold increase that results from doubling the dimensions of the rectangular solid.

Conclusion

Doubling the edge lengths of a rectangular solid results in a surface area that is four times greater than the original. With the correct calculations, the new surface area of 304 square inches accurately reflects this increase, while the other choices demonstrate misunderstandings of how surface area relates to dimensional changes. Thus, understanding the properties of geometric scaling is crucial for solving such problems accurately.

If the lengths of all the edges of the rectangular solid in the preceding figurewere doubled, what would be the surface area, in square inches, of the new rectangular solid?

The surface area of the new rectangular solid would be 304 square inches.

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