Final answer:
Doubling all linear dimensions of a right prism quadruples the surface area. Each face's area increases by a factor of four since the surface area is proportional to the square of the linear dimensions.
Step-by-step explanation:
When doubling all the linear dimensions of a right prism with original dimensions 5 in., 4 in., and 17 in., we need to consider the effect this change will have on the area. Doubling each dimension changes the dimensions of the prism to 10 in., 8 in., and 34 in. respectively. To find the new surface area, we calculate the area of each face and sum them up. Each face of the prism is a rectangle, and since there are two of each unique face in a right prism, the total surface area is the sum of the areas of each pair of faces.
Originally, the faces have the following areas: two faces are 5×4 in., two faces are 4×17 in., and two faces are 5×17 in. After doubling the dimensions, the new face areas are: two faces are 10×8 in., two faces are 8×34 in., and two faces are 10×34 in. The surface area of each face is quadrupled because the area is proportional to the square of the linear dimensions (Area ≈ Length²).
Thus, if the original surface area is 'A', the new surface area after doubling the dimensions will be '4A', which means the correct answer is (a) Surface area becomes 4 × the original. This can be confirmed by calculating the original and new surface areas and comparing them.