Rectangular prism A has a surface area of 25 square units and rectangular prism B has a surface area of 100 square units. Which statement accurately compares the dimensions of prism A to those of prism B ?(1 point) Responses Since prism B ’s surface area is 4 times as large as prism A ’s surface area, prism B ’s dimensions are half as large as prism A ’s. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are half as large as prism upper A ’s. Since prism B ’s surface area is 4 times as large as prism A ’s surface area, prism B ’s dimensions are 8 times as large as prism A ’s. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are 8 times as large as prism upper A ’s. 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. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are twice as large as prism upper A ’s. Since prism B ’s surface area is 4 times as large as prism A ’s surface area, prism B ’s dimensions are 16 times as large as prism A ’s.

Answer 1

To accurately compare the dimensions of prism A to prism B based on their surface areas, we can use the relationship between the surface area of similar geometric figures and their linear dimensions.

The surface area \(S\) of a rectangular prism can be calculated using the formula: \[ S = 2(ab + ac + bc) \] where \(a\), \(b\), and \(c\) are the dimensions of the prism.

If surface area increases by a factor of \(k\) (in this case, \(k = 4\) since \(100 / 25 = 4\)), then the dimensions of the prisms relate to the square root of this factor because surface area involves dimensions squared.

Thus, if the surface area of prism B is 4 times that of prism A, then the dimensions of prism B are scaled by \(\sqrt{4}\), which is \(2\).

Using this reasoning, the correct statement is: "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."