44. 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?
Answer: C
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. If the original surface area was 76 square inches, doubling the dimensions results in a new surface area of 304 square inches.
A) 152
This option is incorrect because it suggests a surface area that is less than the original solid's surface area. Doubling the dimensions of the solid should increase the surface area, not decrease it.
B) 160
This option is also incorrect. While it represents an increase, it does not account for the correct factor of four increase in surface area that occurs when all dimensions are doubled.
C) 304
This is the correct answer. When the dimensions of the rectangular solid are doubled, the surface area is calculated by multiplying the original surface area by four, leading to a final surface area of 304 square inches.
D) 320
This option is incorrect, as it overestimates the surface area after the dimensions have been doubled. The correct calculation yields 304 square inches, not 320.
Conclusion
The correct answer of 304 square inches reflects the proper calculation of surface area when the dimensions of a rectangular solid are doubled, confirming that all other options fail to provide the accurate result based on the geometric principles involved. Understanding how surface area scales with dimension changes is essential in solving such problems.