The statement that "since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are twice as large as prism A’s" is not accurate.
The surface area of a rectangular prism (or box) is calculated using the formula: \[ SA = 2(lw + lh + wh) \] where \( l \), \( w \), and \( h \) are the length, width, and height of the prism, respectively.
If prism B has a surface area that is 4 times that of prism A, then we can infer the following:
- The surface area ratio of the two prisms is: \[ \frac{SA_B}{SA_A} = \frac{100}{25} = 4 \]
However, the dimensions do not scale linearly with surface area. When the dimensions of an object are scaled by a factor of \( k \), the surface area scales by \( k^2 \).
Therefore, if the surface area of prism B is 4 times that of prism A, the dimensions of prism B must be scaled by a factor of \( k \) where \( k^2 = 4 \). This gives \( k = 2 \).
Thus, the correct interpretation is that the dimensions of prism B are twice as large as those of prism A. So, the statement, although it may seem somewhat ambiguous due to the wording, is fundamentally correct: prism B’s dimensions are indeed twice as large as prism A's dimensions.
So, the final conclusion is:
- True: Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are twice as large as prism A’s.