4. A shipping box for a refrigerator is shaped like a rectangular prism. The box has a depth of 34.25 inches (in.), a height of 69.37 in., and a width of 32.62 in. To the nearest hundredth cubic inch, what is the volume of the shipping bax?
Answer: B
The volume of the shipping box is 77,502.59 cubic inches.
To find the volume of a rectangular prism, you multiply its depth, height, and width. In this case, multiplying 34.25 in. (depth) by 69.37 in. (height) by 32.62 in. (width) yields a volume of 77,502.59 cubic inches.
A) 2,262.85
This option is incorrect as it significantly underestimates the volume of the shipping box. The volume calculation involves multiplying three dimensions which results in a much larger figure than 2,262.85 cubic inches.
B) 77,502.59
This is the correct answer. Calculating the volume by multiplying the dimensions 34.25 in., 69.37 in., and 32.62 in. results in exactly 77,502.59 cubic inches, confirming this option as accurate.
C) 136.24
This option is also incorrect as it drastically underrepresents the volume of the shipping box. The calculated volume should be in the tens of thousands, making 136.24 cubic inches not a plausible measurement for this shipping box.
D) 25,834.20
While this option is larger than some other incorrect choices, it still does not match the calculated volume of the box. The dimensions yield a volume much greater than 25,834.20 cubic inches, indicating this option is also incorrect.
Conclusion
The correct answer of 77,502.59 cubic inches is derived from accurately multiplying the box's dimensions, confirming that the other options fail to represent the true volume of the shipping box. Both A and C are too low, while D, despite being higher, still does not reach the correct volume. Hence, B is definitively the right choice.